HOLOGRAPHIC QUENCHES WITH A GAPentangle2016/PLopez.pdfAdS boundary AdS3 with an IR cutoff + massless...
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HOLOGRAPHIC
QUENCHES WITH A GAP
Esperanza Lopez
together with E. da Silva, J. Mas and A. Serantes, arXiv:1604. 08765
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩
holographic thermalization
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩
holographic thermalization
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩
holographic thermalization
reflecting boundary
bouncing geometries in AdS(Bizon, Rostworowski 2011; Buchel, Lehner, Liebling, 2012;......)
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩
holographic thermalization
reflecting boundary
bouncing geometries in AdS(Bizon, Rostworowski 2011; Buchel, Lehner, Liebling, 2012;......)
quantum quench
Quenches & revivals in holography
H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H
revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩
↕ (Abajo, da Silva, Lopez, Mas, Serantes, 2014)
Outlook
holographic quenches: H ≠ H0
Outlook
holographic quenches: H ≠ H0
compare the parameter space for revivals and oscillating geometries
Outlook
holographic quenches: H ≠ H0
compare the parameter space for revivals and oscillating geometries
typical versus fine-tuned initial state and its holographic representation
Outlook
holographic quenches: H ≠ H0
compare the parameter space for revivals and oscillating geometries
typical versus fine-tuned initial state and its holographic representation
compare with results from other approaches: tensor networks
The model
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
D,N boundary conditions at the wall
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
energy is conserved at the IR wall
D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
energy is conserved at the IR wall time dependent profiles at the wall
redistribution of energy between metric and scalar
D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)
quench dynamics of a 1+1 massive QFT
The model AdS boundary
IR hard wallAdS3 with an IR cutoff + massless scalar
energy is conserved at the IR wall time dependent profiles at the wall
redistribution of energy between metric and scalar
Δt < IR scale out of equilibrium
D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)
quench dynamics of a 1+1 massive QFT
Static solutions with Φ=0
ds
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
AdS-hard wall
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
AdS-hard wall
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
M0 z0 >1 : black hole2
AdS-hard wall
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
M0 z0 >1 : black hole2
M0 z0 <1 : AdS, AdS-BH, naked singularities2
AdS-hard wall
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
M0 z0 >1 : black hole2
M0 z0 <1 : AdS, AdS-BH, naked singularities2 M0: wall mass
AdS-hard wall
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
M0 z0 >1 : black hole2
M0 z0 <1 : AdS, AdS-BH, naked singularities2
no reason to exclude M0<0
M0: wall mass
AdS-hard wall
= 1
Static solutions with Φ=0
AdS boundary: Minkowskids
2 =1z
2
✓�(1�M0z
2) dt
2 +dz
2
1�M0z2
+ dx
2
◆
M0=0 : AdS3
M0>0 : black hole
M0<0 : naked singularity
z0
M0 z0 >1 : black hole2
M0 z0 <1 : AdS, AdS-BH, naked singularities2
no reason to exclude M0<0
M0: wall mass
Solitonic solutionsDirichlet bc at the wall :
static solutions with a non-trivial scalar profile
Solitonic solutionsDirichlet bc at the wall :
static solutions with a non-trivial scalar profile
solitons up to a threshold Φ0 (M0)
stable and unstable branches
stable solitons with M>1
given M0MXO\
0.2 0.4 0.6 0.8 1.0 1.2f0
0.2
0.4
0.6
0.8
1.0
1.2
•
•
:op dual to Φ
:total mass
Φ0 : scalar field at the wall
Solitonic solutionsDirichlet bc at the wall :
static solutions with a non-trivial scalar profile
-20 -15 -10 -5M0
-2
-1
1
2
f0parameter space
solitons up to a threshold Φ0 (M0)
stable and unstable branches
stable solitons with M>1
given M0MXO\
0.2 0.4 0.6 0.8 1.0 1.2f0
0.2
0.4
0.6
0.8
1.0
1.2
•
•
:op dual to Φ
:total mass
Φ0 : scalar field at the wall
Solitonic solutionsDirichlet bc at the wall :
static solutions with a non-trivial scalar profile
-20 -15 -10 -5M0
-2
-1
1
2
f0parameter space
boundary conditions can not be changed by bulk dynamics
solitons = vacua { M0 ,Φ0 } = couplings
solitons up to a threshold Φ0 (M0)
stable and unstable branches
stable solitons with M>1
given M0MXO\
0.2 0.4 0.6 0.8 1.0 1.2f0
0.2
0.4
0.6
0.8
1.0
1.2
•
•
:op dual to Φ
:total mass
Φ0 : scalar field at the wall
Mass gap
lowest pole of 2-point function
Mass gap
⇒ normal modes of Φlowest pole of 2-point function
Mass gap
⇒ normal modes of Φ
M0 ,Φ0 ≠ 0 break Lorentz invariance
field theory in a non-trivial homogeneous medium
lowest pole of 2-point function
Mass gap
⇒ normal modes of Φ
M0 ,Φ0 ≠ 0 break Lorentz invariance
field theory in a non-trivial homogeneous medium ≤ 1dωdk
causality
lowest pole of 2-point function
Mass gap
⇒ normal modes of Φ
M0 ,Φ0 ≠ 0 break Lorentz invariance
field theory in a non-trivial homogeneous medium ≤ 1dωdk
causality
lowest pole of 2-point function
mgap = ω| for the lowest normal modek=0
Mass gap
⇒ normal modes of Φ
M0 ,Φ0 ≠ 0 break Lorentz invariance
field theory in a non-trivial homogeneous medium ≤ 1dωdk
causality
lowest pole of 2-point function
M0=1/2
M0=-8
the gap increases with negative M0, closes up with growing Φ0
mgap = ω| for the lowest normal modek=0
Entanglement entropy
A
B
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
S(l>ξ ) = const
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
S(l>ξ ) = const
l homologous to γS(l )∝ length(γ)
holographic entanglement entropy
γ
IR wall
• •l
(Ryu, Takayanagi, 2006)
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
homology relative to IR wall
S(l>ξ ) = const
l homologous to γS(l )∝ length(γ)
holographic entanglement entropy
γ
IR wall
• •l
(Ryu, Takayanagi, 2006)
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
homology relative to IR wall
S(l>ξ ) = const
l homologous to γS(l )∝ length(γ)
holographic entanglement entropy
γ
IR wall
• •l
(Ryu, Takayanagi, 2006)
S(A)= - Tr ρA log ρA
Entanglement entropy
A
B
Area law
S(A)∝ ∂A
ξ : correlation length
1+1 gapped theory
• •l
homology relative to IR wall
S(l>ξ ) = const
pure state S(A)=S(B) in the absence of horizons: pure states
l homologous to γS(l )∝ length(γ)
holographic entanglement entropy
γ
IR wall
• •l
(Ryu, Takayanagi, 2006)
S(A)= - Tr ρA log ρA
Correlation length
γγ
ll
Correlation length
S(l )∝log(l )
γγ
ll
Correlation length
S(l )∝log(l ) S(l )=const
γγ
ll
Correlation length
S(l )∝log(l ) S(l )=const
ξ length(con)=length(dis) γγ
ll
Correlation length
S(l )∝log(l ) S(l )=const
ξ length(con)=length(dis) γγ
ll
M0=1/2
M0=-8
ξ decreases with negative M0, increases with Φ0
Correlation length
S(l )∝log(l ) S(l )=const
ξ length(con)=length(dis) γγ
ll
expected: mgap ξ = O(1)
M0=1/2
M0=-8
ξ decreases with negative M0, increases with Φ0
Correlation length
S(l )∝log(l ) S(l )=const
ξ length(con)=length(dis) γγ
ll
expected: mgap ξ = O(1)
except close to soliton threshold:large N effect
M0=1/2
M0=-8
◉
0.0 0.5 1.0 1.5 2.0f0
1
2
3
4
5
6
7
xw
M0=-∞
M0=1/2
M0=-8
ξ decreases with negative M0, increases with Φ0
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
dirichlet bc : �̇0 = 0
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
⇧ ⌘ A�1e��̇
⇧0 =
✏
↵
1
cosh
2 t/↵ → time dependent wall profile : dirichlet bc : �̇0 = 0
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
⇧ ⌘ A�1e��̇
⇧0 =
✏
↵
1
cosh
2 t/↵ → time dependent wall profile :
M = M0 + MΦ = const
⤷
⤶
energy exchange
dirichlet bc : �̇0 = 0
ËË
-12 -10 -8 -6 -4 -2M0
-2
-1
1
2
f0
◉
shorter time span
initial state
growing amplitude
Holographic quench
simple gapped model with 2 couplings, which control IR physics
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
ds
2 =1z
2
✓�A(t, z)e�2�(t,z)
dt
2 +dz
2
A(t, z)+ dx
2
◆, �(t, z)
⇧0 =
✏
↵
1
cosh
2 t/↵
⇧ ⌘ A�1e��̇
⇧0 =
✏
↵
1
cosh
2 t/↵ → time dependent wall profile :
M = M0 + MΦ = const
⤷
⤶
energy exchange
M<1 : ever bouncing
dirichlet bc : �̇0 = 0
ËË
-12 -10 -8 -6 -4 -2M0
-2
-1
1
2
f0
◉
shorter time span
initial state
growing amplitude
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
energy density < ( infrared scale )
# fieldsd
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
energy density < ( infrared scale )
# fieldsd
global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
energy density < ( infrared scale )
# fieldsd
global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d
AdS3 hard wall
Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
energy density < ( infrared scale )
# fieldsd
global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d
√Mcollapse - Mgs ≲ infrared scale
AdS3 hard wall
Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}
Revivals versus bounces
when to expect revivals? interactions disfavor revivals, except
energy density < ( infrared scale )
# fieldsd
global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d
√Mcollapse - Mgs ≲ infrared scale
AdS3 hard wall
Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}
M0=-∞◉
M0=-8
M0=1/2
0.5 1.0 1.5 2.0f0
0.1
0.2
0.3
0.4
0.5
DM êw
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
parameters of the wall action : α (time span), ε (amplitude)
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
parameters of the wall action : α (time span), ε (amplitude)
α = √gtt α~ __↓
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
parameters of the wall action : α (time span), ε (amplitude)
α = √gtt α~ __↓
α >1: adiabatic change~-20 -15 -10 -5M0
-2
-1
1
2
f0
-20 -15 -10 -5M0
-2
-1
1
2
f0
⤴••
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
parameters of the wall action : α (time span), ε (amplitude)
α = √gtt α~ __↓
α >1: adiabatic change~-20 -15 -10 -5M0
-2
-1
1
2
f0
-20 -15 -10 -5M0
-2
-1
1
2
f0
⤴••
α <1: radial localization~
MΦ=∫ρdz
Decoding oscillating geometriesassociated field theory state mechanism behind revivals
parameters of the wall action : α (time span), ε (amplitude)
α = √gtt α~ __↓
α >1: adiabatic change~-20 -15 -10 -5M0
-2
-1
1
2
f0
-20 -15 -10 -5M0
-2
-1
1
2
f0
⤴••
α <1: radial localization~
MΦ=∫ρdz
α ≈1: standing wave~
α = 0.8
α = 0.2
Energy density
M-Mgs
M-Mgse = _
energy density above vacuum normalized to that for fast
thermalization
Energy density
M-Mgs
M-Mgse = _
energy density above vacuum normalized to that for fast
thermalization
α ≈ 1: e ≪ 1
α < 1: e ≲ 1~
~
Energy density
M-Mgs
M-Mgse = _
energy density above vacuum normalized to that for fast
thermalization
α ≈ 1: e ≪ 1
α < 1: e ≲ 1~
~
Periodicity
α ≈ 1: periodicity of lowest normal mode
~2πωτ ≈
Energy density
M-Mgs
M-Mgse = _
energy density above vacuum normalized to that for fast
thermalization
α ≈ 1: e ≪ 1
α < 1: e ≲ 1~
~
Periodicity
α ≈ 1: periodicity of lowest normal mode
~2πωτ ≈
α < 1: different periodicity~
larger far from stability threshold
Tensor networks
variational ansatz for QFT states based on entanglement properties
• ↑↓| i =X
ci1i2. . . iN |i1i2. . . iN i • • ••• • ••• ••••
Tensor networks
variational ansatz for QFT states based on entanglement properties
• ↑↓| i =X
ci1i2. . . iN |i1i2. . . iN i
matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN
• • ••• • ••• ••••
A | | | | | |
A A A A A (❨ (❨
Tensor networks
variational ansatz for QFT states based on entanglement properties
• ↑↓| i =X
ci1i2. . . iN |i1i2. . . iN i
matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN
• • ••• • ••• ••••
A | | | | | |
A A A A A (❨ (❨
2 → 2 (rank Ai) N 2
Tensor networks
variational ansatz for QFT states based on entanglement properties
• ↑↓| i =X
ci1i2. . . iN |i1i2. . . iN i
matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN
• • ••• • ••• ••••
A | | | | | |
A A A A A (❨ (❨
area law
2 → 2 (rank Ai) N 2
Tensor networks
variational ansatz for QFT states based on entanglement properties
• ↑↓| i =X
ci1i2. . . iN |i1i2. . . iN i
matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN
• • ••• • ••• ••••
A | | | | | |
A A A A A (❨ (❨
area law
2 → 2 (rank Ai) N 2
Schwinger model ground state, low lying spectrum
(Pichler et al 2015; Buyens et al, 2014,2016)
(Banuls,Cichy,Jansen,Cirac, 2013; Rico et al, 2013)
real time simulations: Schwinger mechanism, quenches
Schwinger model quench massive Schwinger model + quench: turn on abruptly an electric field
(Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
Schwinger model quench
pair production: energy density ~ fermion mass
massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
Schwinger model quench
pair production: energy density ~ fermion mass
oscilations of electric field & particle number (out of phase)
small energies : revivals
(Buyens et al)
massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
Schwinger model quench
pair production: energy density ~ fermion mass
oscilations of electric field & particle number (out of phase)
small energies : revivals
(Buyens et al)
massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
oscilations of entanglement entropy
Schwinger model quench
pair production: energy density ~ fermion mass
small energy limit : perfect revivals
τ ≈ 2πΔm
Δm : mass of lowest stable excitation
oscilations of electric field & particle number (out of phase)
small energies : revivals
(Buyens et al)
massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
oscilations of entanglement entropy
Schwinger model quench
pair production: energy density ~ fermion mass
small energy limit : perfect revivals
τ ≈ 2πΔm
Δm : mass of lowest stable excitation
|�i =X an
pn!
e�in�mt|ni
oscilations of electric field & particle number (out of phase)
small energies : revivals
(Buyens et al)
massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)
oscilations of entanglement entropy
On the holographic interpretation
holographic model: # fields >>1
Schwinger model: # fields ~1
On the holographic interpretation
BUT revivals depend on energy density
# fields
holographic model: # fields >>1
Schwinger model: # fields ~1
On the holographic interpretation
pairs of entangled quasiparticles
(Cardy,Calabrese, 2005)
stronger correlations when emitted at close points
entangled pairs stream away at c=1
xt=0
t
simple picture of massive to massless quench
BUT revivals depend on energy density
# fields
holographic model: # fields >>1
Schwinger model: # fields ~1
On the holographic interpretation
pairs of entangled quasiparticles
(Cardy,Calabrese, 2005)
stronger correlations when emitted at close points
entangled pairs stream away at c=1
xt=0
t
simple picture of massive to massless quench
l>2t
γ
l
BUT revivals depend on energy density
# fields
holographic model: # fields >>1
Schwinger model: # fields ~1
(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)
On the holographic interpretation
pairs of entangled quasiparticles
(Cardy,Calabrese, 2005)
stronger correlations when emitted at close points
entangled pairs stream away at c=1
xt=0
t
simple picture of massive to massless quench
l>2t
γ
l
l
γ
l<2t
BUT revivals depend on energy density
# fields
holographic model: # fields >>1
Schwinger model: # fields ~1
(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)
On the holographic interpretation
shell infall drift away of entangled excitations
pairs of entangled quasiparticles
(Cardy,Calabrese, 2005)
stronger correlations when emitted at close points
entangled pairs stream away at c=1
xt=0
t
simple picture of massive to massless quench
l>2t
γ
l
l
γ
l<2t
BUT revivals depend on energy density
# fields
holographic model: # fields >>1
Schwinger model: # fields ~1
(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
momentum zero coherent state
→ no radial displacement
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
momentum zero coherent state
→ no radial displacement
~α ≈ 1
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
momentum zero coherent state
→ no radial displacement
~α ≈ 1
electric field ↓
vev of O
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
momentum zero coherent state
→ no radial displacement
~α ≈ 1
electric field ↓
vev of O
Comparing with AdS-HW
lowest excitation Δm → lowest normal mode
small energy quench maps to standing scalar pulse
momentum zero coherent state
→ no radial displacement
~α ≈ 1
2 4 6 8t
-6
-4
-2
2
4
6
XO\
α < 1 ~
electric field ↓
vev of O
Increasing the quench energy
resulting state should contain finite momentum modes
oscillating pulse must involve radial displacement
Increasing the quench energy
resulting state should contain finite momentum modes
oscillating pulse must involve radial displacement
check 1
ò
ô
0.0 0.2 0.4 0.6 0.8 1.0z
2
4
6
8
10r
e=0.28
e=0.7
α = .2~
Increasing the quench energy
resulting state should contain finite momentum modes
oscillating pulse must involve radial displacement
check 1
ò
ô
0.0 0.2 0.4 0.6 0.8 1.0z
2
4
6
8
10r
e=0.28
e=0.7
α = .2~
check 2 Φ=Φsol + ε lowest normal mode
Increasing the quench energy
resulting state should contain finite momentum modes
oscillating pulse must involve radial displacement
check 1
ò
ô
0.0 0.2 0.4 0.6 0.8 1.0z
2
4
6
8
10r
e=0.28
e=0.7
α = .2~radial localization increases with energy
e=0.5ô
ò
0.0 0.2 0.4 0.6 0.8 1.0z
2
4
6
8
10r
check 2 Φ=Φsol + ε lowest normal mode
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
δt → 0 : singular configuration
(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
same for a wall variation of bc
δt → 0 : singular configuration
(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
finite energy quench → radial localization ~ energy
same for a wall variation of bc
δt → 0 : singular configuration
(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
finite energy quench → radial localization ~ energy
rising energy ~ increasing radial localization
same for a wall variation of bc
δt → 0 : singular configuration
(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)
different dynamics of thin and broad shells
The holographic dual of a quench
quench: sudden action abrupt time variation of boundary conditions
varying bc at AdS3 boundary shell mass ∝ εδt
2
2 shell thickness ∝ δt
finite energy quench → radial localization ~ energy
revivals ~ standing waves rising energy ~ increasing radial localization
same for a wall variation of bc
δt → 0 : singular configuration
(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)
different dynamics of thin and broad shells
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲thin shells of small
mass are not typical
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲thin shells of small
mass are not typical
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲
able to resolve scales smaller than IR gap
thin shells of small mass are not typical
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲
able to resolve scales smaller than IR gap
energy density < gap
# fields2
thin shells of small mass are not typical
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲
able to resolve scales smaller than IR gap
energy density < gap
# fields2 not enough for Schwinger mechanism
virtual pairs can not separate further than ξ
thin shells of small mass are not typical
“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?
no fine tuning involved↲
able to resolve scales smaller than IR gap
energy density < gap
# fields2 not enough for Schwinger mechanism
virtual pairs can not separate further than ξ
thin shells of small mass are not typical
high energy
low energy
Conclusions
discuss general aspects of the holographic modeling of quenches using a simple setup
Conclusions
discuss general aspects of the holographic modeling of quenches using a simple setup
qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells
Conclusions
discuss general aspects of the holographic modeling of quenches using a simple setup
needed a further QFT understanding of small mass localized pulses
qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells
Conclusions
discuss general aspects of the holographic modeling of quenches using a simple setup
needed a further QFT understanding of small mass localized pulses
qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells
real time simulations have become recently accessible with tensor network techniques; holography provides a conceptually and perhaps also practical interesting alternative
Conclusions
discuss general aspects of the holographic modeling of quenches using a simple setup
needed a further QFT understanding of small mass localized pulses
qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells
real time simulations have become recently accessible with tensor network techniques; holography provides a conceptually and perhaps also practical interesting alternative
Thanks