Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Piroli, L., Vernier, E., Pasquale Calabrese, Balázs Pozsgay

Published Jun 19, 2019• 51 citations
OpenAlex

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.

Related papers

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

Lorenzo Piroli, Eric Vernier, Pasquale Calabrese +1 more

Abstract We consider quantum quenches in the integrable -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:1811.00432•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2019•36 citations

Exact solution for the quench dynamics of a nested integrable system

Márton Mestyán, Bruno Bertini, Lorenzo Piroli +1 more

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has been focusing on models with an elementary (i.e., not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the Quench Action approach. Specifically, we consider the spin-$1$ Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

•Jan 1, 2017•66 citations

Exact solution for the quench dynamics of a nested integrable system

Márton Mestyán, Bruno Bertini, Lorenzo Piroli +1 more

Abstract Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai–Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

arXiv:1705.00851•Journal of Statistical Mechanics Theory and Experiment•Aug 1, 2017•61 citations

Integrable quenches in nested spin chains II: the Quantum Transfer Matrix approach

Lorenzo Piroli, Eric Vernier, Pasquale Calabrese +1 more

We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain fused operators that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the $T$- and $Y$-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of $SU(3)$-invariant Hamiltonians with open boundary conditions.

•Dec 13, 2018•8 citations

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Lorenzo Piroli, Eric Vernier, Pasquale Calabrese +1 more

Abstract We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to ‘soliton-non-preserving’ boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain ‘fused operators’ that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T - and Y -systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.

arXiv:1812.05330•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2019•24 citations

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Piroli, L., Vernier, E., Pasquale Calabrese +1 more

We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to 'soliton-non-preserving' boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain 'fused operators' that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T- and Y-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.

•Jun 19, 2019•36 citations
We consider quantum quenches in the integrable SU(3)SU(3)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.
Abstract We consider quantum quenches in the integrable -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.
Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has been focusing on models with an elementary (i.e., not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the Quench Action approach. Specifically, we consider the spin-111 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.
Abstract Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai–Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.
We consider quantum quenches in the integrable SU(3)SU(3)SU(3)-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain fused operators that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the TTT- and YYY-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of SU(3)SU(3)SU(3)-invariant Hamiltonians with open boundary conditions.
Abstract We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to ‘soliton-non-preserving’ boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain ‘fused operators’ that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T - and Y -systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.
We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to 'soliton-non-preserving' boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain 'fused operators' that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T- and Y-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.