scholarly journals Entanglement evolution and generalised hydrodynamics: interacting integrable systems

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Vincenzo Alba ◽  
Bruno Bertini ◽  
Maurizio Fagotti
Keyword(s):  
Integrable Systems ◽  
Entanglement Entropy ◽  
Integrable Models ◽  
Analytical Prediction ◽  
Bipartite Entanglement ◽  
Entanglement Evolution ◽  
Thermodynamic Entropy ◽  
Quasiparticle Picture

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.

scholarly journals Entanglement and thermodynamics after a quantum quench in integrable systems

2017 ◽  
Vol 114 (30) ◽  
pp. 7947-7951 ◽  
Author(s):  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Scaling Limit ◽  
Entanglement Dynamics ◽  
Entanglement Evolution ◽  
Thermodynamic Entropy ◽  
Time Scaling ◽  
Quantum Quenches ◽  
Zero Entropy ◽  
Local Properties ◽  
Isolated Systems ◽  
Quasiparticle Picture

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space–time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.

scholarly journals Entanglement spreading in non-equilibrium integrable systems

2020 ◽  
Author(s):  
Pasquale Calabrese
Keyword(s):  
Summer School ◽  
Condensed Matter ◽  
Entanglement Entropy ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Equilibrium Dynamics ◽  
Thermodynamic Entropy ◽  
Short Course ◽  
Quasiparticle Picture ◽  
Non Equilibrium

These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength.

scholarly journals ALGEBRAIC ASPECT AND CONSTRUCTION OF LAX OPERATORS IN QUANTUM INTEGRABLE SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3113-3117 ◽  
Author(s):  
B. BASU-MALLICK ◽  
ANJAN KUNDU
Keyword(s):  
Integrable Systems ◽  
Integrable Models ◽  
Quantum Integrable Systems ◽  
Algebraic Construction ◽  
Algebraic Aspect ◽  
Quantum Integrable Models

An algebraic construction which is more general and closely connected with that of Faddeev,1 along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

scholarly journals Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder

2019 ◽  
Vol 52 (23) ◽  
pp. 235202 ◽  
Author(s):  
Vincent Beaud ◽  
Julian Sieber ◽  
Simone Warzel
Keyword(s):  
Entanglement Entropy ◽  
Bipartite Entanglement

scholarly journals Generic Entanglement Entropy for Quantum States with Symmetry

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 684
Author(s):  
Yoshifumi Nakata ◽  
Mio Murao
Keyword(s):  
Phase Transition ◽  
Information Science ◽  
Entanglement Entropy ◽  
Quantum States ◽  
Permutation Symmetry ◽  
Phase Transition Behavior ◽  
Bipartite Entanglement ◽  
Translation Symmetry ◽  
The One ◽  
Random States

When a quantum pure state is drawn uniformly at random from a Hilbert space, the state is typically highly entangled. This property of a random state is known as generic entanglement of quantum states and has been long investigated from many perspectives, ranging from the black hole science to quantum information science. In this paper, we address the question of how symmetry of quantum states changes the properties of generic entanglement. More specifically, we study bipartite entanglement entropy of a quantum state that is drawn uniformly at random from an invariant subspace of a given symmetry. We first extend the well-known concentration formula to the one applicable to any subspace and then show that 1. quantum states in the subspaces associated with an axial symmetry are still highly entangled, though it is less than that of the quantum states without symmetry, 2. quantum states associated with the permutation symmetry are significantly less entangled, and 3. quantum states with translation symmetry are as entangled as the generic one. We also numerically investigate the phase-transition behavior of the distribution of generic entanglement, which indicates that the phase transition seems to still exist even when random states have symmetry.

scholarly journals HYPER-KÄHLER METRICS BUILDING AND INTEGRABLE MODELS

1994 ◽  
Vol 09 (34) ◽  
pp. 3163-3173 ◽  
Author(s):  
E.H. SAIDI ◽  
M.B. SEDRA
Keyword(s):  
Integrable Systems ◽  
Constraint Equation ◽  
Integrable Models ◽  
Explicit Solutions ◽  
Harmonic Superspace ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Conserved Currents

Methods developed for the analysis of integrable systems are used to study the problem of hyper-Kähler metrics building as formulated in D=2, N=4 supersymmetric harmonic superspace. We show in particular that the constraint equation [Formula: see text] and its Toda-like generalizations are integrable. Explicit solutions together with the conserved currents generating the symmetry responsible for the integrability of these equations are given. Other features are also discussed.

scholarly journals ON LIE GROUPS, CLUSTER VARIABLES AND INTEGRABLE SYSTEMS

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340007
Author(s):  
A. MARSHAKOV
Keyword(s):  
Lie Groups ◽  
Integrable Systems ◽  
Explicit Construction ◽  
Integrable Models ◽  
Loop Groups ◽  
Integrals Of Motion ◽  
General Terms

We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.

FROM INHOMOGENEOUS SIX-VERTEX LATTICE MODELS TO CONTINUUM QUANTUM INTEGRABLE MODELS

1992 ◽  
Vol 07 (25) ◽  
pp. 6385-6403
Author(s):  
Y.K. ZHOU
Keyword(s):  
Integrable Systems ◽  
Scaling Limit ◽  
Lattice Models ◽  
Integrable Models ◽  
Two Dimensional ◽  
Vertex Model ◽  
Quantum Integrable Systems ◽  
Vertex Models ◽  
Quantum Integrable Models ◽  
Sine Gordon Model

A method to find continuum quantum integrable systems from two-dimensional vertex models is presented. We explain the method with the example where the quantum sine-Gordon model is obtained from an inhomogeneous six-vertex model in its scaling limit. We also show that the method can be applied to other models.

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