Nonlinear integral equations for thermodynamics of the<i>sl</i>(<i>r</i>  1) Uimin Sutherland model

Tsuboi, Zengo

doi:10.1088/0305-4470/36/5/321

Cited by 17 publications

(58 citation statements)

References 40 publications

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“…Note that the existence of such a functional is a priori non-trivial, as Eq. (93) implies that the overlap between |Ψ 0 and the eigenstates of the Hamiltonian only depends on the set {ρ…”

Section: The Quench Action Methodsmentioning

confidence: 99%

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

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

101

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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:1811.00432v4 [cond-mat.stat-mech]

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“…Note that the existence of such a functional is a priori non-trivial, as Eq. (93) implies that the overlap between |Ψ 0 and the eigenstates of the Hamiltonian only depends on the set {ρ…”

Section: The Quench Action Methodsmentioning

confidence: 99%

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

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

101

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“…The key ingredients of the HTE method are the Quantum Transfer Matrix (QTM) [134,135,136,137,138,139,140,141,142,143] and a functional relation called the T -system [144,145,146], from which one derives nonlinear integral equations which can be solved in an exact perturbative fashion. To date this approach has been applied to the Heisenberg model [129], the osp(1|2s) model [130], the su(N ) Uimin-Lai-Sutherland model [131], the higher spin Heisenberg model [147], the su(N ) Perk-Schultz model [148] and the su(m|n) Perk-Schultz model [149]. In particular, in this way, i.e., via the HTE expansion, it has been demonstrated that the integrable su(4) ladder model can be used to study the thermodynamics and magnetic properties of the strongly coupled ladder compounds [8].…”

Section: Integrable Ladder Modelsmentioning

confidence: 99%

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

Batchelor

Guan

Oelkers

et al. 2007

Advances in Physics

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This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of strong coupling ladder compounds. For this class of compounds the rung coupling J ⊥ is much stronger than the coupling J along the ladder legs. The ground state properties of the integrable two-leg spin-1 2 and the mixed spin-( 1 2 , 1) ladder models at zero temperature are analysed by means of the Thermodynamic Bethe Ansatz (TBA). Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are discussed in terms of the recently introduced High Temperature Expansion (HTE) method, which is reviewed in detail. In the strong coupling region the integrable spin-1 2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime H < H c1 = J ⊥ − 4J , (ii) a fully polarized phase for H > H c2 = J ⊥ + 4J , and (iii) a Luttinger liquid magnetic phase in the regime H c1 < H < H c2 . The critical behaviour in the vicinity of the critical points H c1 and H c2 is of Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for the strong coupling ladder compounds (5IAP) 2 CuBr 4 · 2H 2 O, Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 , (C 5 H 12 N) 2 CuBr 4 , BIP-BNO and [Cu 2 (C 2 O 2 )(C 10 H 8 N 2 ) 2 )](NO 3 ) 2 . Similar analysis of the mixed spin-( 1 2 , 1) ladder model reveals a rich phase diagram, with a 1 3 and a full saturation magnetization plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetization plateau is diminished and a new quantum phase †

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“…This integrable model is interesting from the physical point of view, as it displays different quasi-particle species, each one forming an infinite number of bound states. While many properties of the system at zero and finite temperature are by now well understood [3][4][5][6][7][8], including the knowledge of its correlation functions [9,10], until recently the analytical study of quench problems in this model has been out of our reach. The main reason for this lies in the fact that the solution to the Hamiltonian (1) involves a complicated nested Bethe ansatz [11,12], for which generalizations of recent analytic advances in integrability out of equilibrium [13] are not straightforward, including the string-charge duality [14][15][16][17][18] or the Quench Action method [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

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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 "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 SU (3)-invariant Hamiltonians with open boundary conditions.

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Nonlinear integral equations for thermodynamics of thesl(r 1) Uimin Sutherland model

Cited by 17 publications

References 40 publications

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

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

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

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

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