Integrable quenches in nested spin chains I: the exact steady states

Abstract

We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable ``soliton non-preserving'' boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a Quantum Transfer Matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the Quench Action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states.

arXiv comment45 pages, 7 figures; v3: presentation improved; v4: minor revision

References in corpus (87)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Real time evolution using the density matrix renormalization group
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• A one-dimensional liquid of fermions with tunable spin
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• Entanglement dynamics after quantum quenches in generic integrable systems
• "Light-cone" dynamics after quantum quenches in spin chains
• Families of quasi-local conservation laws and quantum spin transport
• What is an integrable quench?
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• One-point Functions in Defect CFT and Integrability
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Quantum quench in the sine-Gordon model
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• One-point Functions in AdS/dCFT from Matrix Product States
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• From Interacting Particles to Equilibrium Statistical Ensembles
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Entanglement and quantum transport in integrable systems
• Quench action and Renyi entropies in integrable systems
• AdS/dCFT one-point functions of the SU(3) sector
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Scalar one-point functions and matrix product states of AdS/dCFT
• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Exactly conserved quasilocal operators for the XXZ spin chain
• Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Overlaps after quantum quenches in the sine-Gordon model
• On the theory of quantum quenches in near-critical systems
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Surface free energy of the open XXZ spin-1/2 chain
• Exact solution for the quench dynamics of a nested integrable system
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Overlaps of Partial Neel States and Bethe States
• Bulk and Boundary S Matrices for the SU(N) Chain
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Quantum spin chain with "soliton non-preserving" boundary conditions
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Excited state correlations of the finite Heisenberg chain
• The quench action approach in finite integrable spin chains
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• Overlap singularity and time evolution in integrable quantum field theory
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries
• Low-Temperature Thermodynamics of $A_2^{(2)}$ and su(3)-invariant Spin Chains
• Monitoring squeezed collective modes of a one-dimensional Bose gas after an interaction quench using density ripples analysis
• Stationary state after a quench to the Lieb-Liniger from rotating BECs
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• A method for solve integrable $A_2$ spin chains combining different representations
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Integrable su(3) spin chain combining different representations
• Anti-Symmetrically Fused Model and Non-Linear Integral Equations in the Three-State Uimin-Sutherland Model
• Fusion and Analytical Bethe Ansatz for the $A_{\n-1}^{(1)}$ Open Spin Chain
• Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
• Quantum quenches in integrable systems: Constraints from factorisation

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• Quantum information scrambling after a quantum quench
• Entanglement spreading in non-equilibrium integrable systems
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
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• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
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• Boundary state bootstrap and asymptotic overlaps in AdS/dCFT
• Crosscap States in Integrable Field Theories and Spin Chains
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• Integrable quenches in the Hubbard model
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• Quantum many-body scars in spin models with multibody interactions
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Time Evolution of Uniform Sequential Circuits
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Generalized hydrodynamics of integrable quantum circuits
• Y-Systems for Generalised Gibbs Ensembles in Integrable Quantum Field Theory
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains
• Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas