Insights into Information Propagation in Long-Range Interacting Quantum Systems
Information propagation in
long-range interacting
quantum systems
Mathias Van Regemortel
, Dries Sels, Michiel Wouters
Reference article
: Mathias Van Regemortel, Dries Sels, and Michiel Wouters
Phys. Rev. A 93, 032311 (2016)
Quantum Quenches
•
We kick the system out of
equilibrium
•
Unitary dynamics
•
In general the system is
not
in
an eigenstate of H
2
Isolated quantum system:
Quantum Quenches
Central questions
:
•
How fast can information be exchanged between
distant points?
•
How does the system relax again after the
quench?
•
What is the equilibrium ensemble after
relaxation?
3
The protocol:
The Lieb-Robinson Bound
4
5
L
Short-range
interactions
Bound on commutator:
Bound on correlation function:
(Lieb Robinson ‘72)
(PRL
’
97 Bravyi, Hastings, Verstraete)
Emergent light cone, effective locality
6
L
Quasiparticle view
(Calabrese, Cardy ‘05)
After quench
quasiparticles
start travelling at
speed c through
system
Experiment
•
One-dimensional
quantum gas in
optical lattice
7
M
C
h
e
n
e
a
u
e
t
a
l
.
N
a
t
u
r
e
4
8
1
,
4
8
4
-
4
8
7
(
2
0
1
2
)
d
o
i
:
1
0
.
1
0
3
8
/
n
a
t
u
r
e
1
0
7
4
8
8
L
Short-range
interactions
Bound on commutator:
Bound on correlation function:
(Lieb Robinson ‘72)
(PRL
’
97 Bravyi, Hastings, Verstraete)
Emergent light cone, effective locality
0
Long-range interactions
•
Hamiltonian with interactions
•
Ubiquitous in nature, e.g. Coulomb interaction
•
Can be implemented with trapped ions:
9
P
R
i
c
h
e
r
m
e
e
t
a
l
.
N
a
t
u
r
e
5
1
1
,
1
9
8
-
2
0
1
(
2
0
1
4
)
d
o
i
:
1
0
.
1
0
3
8
/
n
a
t
u
r
e
1
3
4
5
0
The light cone
10
Michael Foss-Feig et al., Phys. Rev. Lett. 114 (2015)
The Long-Range Kitaev Model
•
J, Δ describes hopping and pairing of fermions
•
Exponent α controls range of long-range pairing interactions
•
Quenches from
•
Exactly solvable model
11
Reference article
: Mathias Van Regemortel, Dries Sels, and Michiel Wouters
Phys. Rev. A 93, 032311 (2016)
12
Quasiparticle velocities
13
•
From the spectrum we
can compute the
quasiparticle velocity
distribution:
•
Divergent group
velocities
•
Yet, most weight inside
well-defined peaks
Mutual information
14
Causality well preserved for LR interactions!
Different systems with LR
interactions
15
L. Cevolani et al., Phys. Rev. A 92, 041603 (2015)
Ising
Bose-Hubbard
Conclusions
•
Lieb-Robinson bounds provide very powerful limits on
information propagation in short-range interacting quantum
systems
•
The Lieb-Robinson bound for long-range interacting
quantum systems is too loose in many cases
•
In the LRK model by far most of the information propagates
inside a well-defined light cone
•
The quasiparticle spectrum allows for a consistent
explanation
•
The physics of long-range interacting quantum systems
seems to be very much model-dependent
16
Reference article
: Mathias Van Regemortel, Dries Sels, and Michiel Wouters
Phys. Rev. A 93, 032311 (2016)
Thank you for your attention!
17
Correlation function
•
α>1: Locality preserved
•
α<1: Power-law decay at
large distances
Light cone:
18
Relaxation after quench
Long-range interactions
allow for slowing down,
rather than speeding up
dynamics!
20
Explore the dynamics of isolated quantum systems through quantum quenches, Lieb-Robinson bounds, and the Transverse Ising Model. Delve into experiments with one-dimensional quantum gases and long-range interactions in Hamiltonians, shedding light on information exchange, relaxation, and equilibrium behaviors.
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Presentation Transcript
Information propagation in long-range interacting quantum systems Mathias Van Regemortel, Dries Sels, Michiel Wouters Reference article: Mathias Van Regemortel, Dries Sels, and Michiel Wouters Phys. Rev. A 93, 032311 (2016)
Quantum Quenches Isolated quantum system: We kick the system out of equilibrium Unitary dynamics In general the system is not in an eigenstate of H 2
Quantum Quenches The protocol: Central questions: How fast can information be exchanged between distant points? How does the system relax again after the quench? What is the equilibrium ensemble after relaxation? 3
L Short-range interactions t L/c 0 Bound on commutator: (Lieb Robinson 72) characteristic velocity c Bound on correlation function: (PRL 97 Bravyi, Hastings, Verstraete) Extra factor 2! Emergent light cone, effective locality 5
L Transverse Ising Model: Quasiparticle view (Calabrese, Cardy 05) After quench quasiparticles start travelling at speed c through system 6
Experiment One-dimensional quantum gas in optical lattice M Cheneau et al. Nature481, 484-487 (2012) doi:10.1038/nature10748 7
L Short-range interactions t L/c 0 Bound on commutator: (Lieb Robinson 72) characteristic velocity c Bound on correlation function: (PRL 97 Bravyi, Hastings, Verstraete) Extra factor 2! Emergent light cone, effective locality 8
Long-range interactions Hamiltonian with interactions Ubiquitous in nature, e.g. Coulomb interaction Can be implemented with trapped ions: P Richerme et al. Nature 511, 198-201 (2014) doi:10.1038/nature13450 9
The light cone Michael Foss-Feig et al., Phys. Rev. Lett. 114 (2015) 10
The Long-Range Kitaev Model J, describes hopping and pairing of fermions Exponent controls range of long-range pairing interactions Quenches from Exactly solvable model Reference article: Mathias Van Regemortel, Dries Sels, and Michiel Wouters Phys. Rev. A 93, 032311 (2016) 11
Quasiparticle velocities From the spectrum we can compute the quasiparticle velocity distribution: Divergent group velocities Yet, most weight inside well-defined peaks 13
Mutual information Causality well preserved for LR interactions! 14
Different systems with LR interactions L. Cevolani et al., Phys. Rev. A 92, 041603 (2015) Ising Bose-Hubbard 15
Conclusions Lieb-Robinson bounds provide very powerful limits on information propagation in short-range interacting quantum systems The Lieb-Robinson bound for long-range interacting quantum systems is too loose in many cases In the LRK model by far most of the information propagates inside a well-defined light cone The quasiparticle spectrum allows for a consistent explanation The physics of long-range interacting quantum systems seems to be very much model-dependent Reference article: Mathias Van Regemortel, Dries Sels, and Michiel Wouters Phys. Rev. A 93, 032311 (2016) 16
Correlation function >1: Locality preserved <1: Power-law decay at large distances Light cone: 18
Relaxation after quench Long-range interactions allow for slowing down, rather than speeding up dynamics!
