Computation of Static Heisenberg-Chain Correlators: Control over Length and Temperature Dependence

Sato, Jun; Aufgebauer, Britta; Boos, H.; Göhmann, Frank; Klümper, Andreas; Takahashi, Minoru; Trippe, Christian

doi:10.1103/physrevlett.106.257201

Cited by 50 publications

(88 citation statements)

References 22 publications

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“…• Connection to the general theory of short range correlators in the fundamental SU (N )-symmetric models. It is known that in the XXZ and XXX Heisenberg spin chains the mean values of all local operators factorize: they can be expressed as combinations of only a few functions, which originate in the two-site density matrix of an inhomogeneous chain [40,41,42,43]. Our previous work [44,6] showed that for the SU (2)-invariant operators of the homogeneous XXX chain these building blocks are identical to the mean values of the currents J 0 α,β .…”

Section: Discussionmentioning

confidence: 99%

Current operators in integrable spin chains: lessons from long range deformations

Pozsgay

2020

SciPost Phys.

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We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU (3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.

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Section: Discussionmentioning

confidence: 99%

Current operators in integrable spin chains: lessons from long range deformations

Pozsgay

2020

SciPost Phys.

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“…Local correlation function are thus expressible as functionals of the quasi-particle densities characterising a macrostate, see e.g. [46][47][48].…”

Section: Equilibrium Ensemblesmentioning

confidence: 99%

The equilibrium landscape of the Heisenberg spin chain

Ilievski

Quinn

2019

SciPost Phys.

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We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

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“…An alternative to the TBA is the Quantum Transfer Matrix (QTM) method [33,34], which leads to a single non-linear integral equation replacing the infinite set of the TBA [35]. Moreover, there are very efficient methods available to compute short-range correlations with the QTM [36,37,38]. The simplicity of the QTM with respect to the TBA makes it an excellent candidate to describe the GGE.…”

Section: Introductionmentioning

confidence: 99%

The generalized Gibbs ensemble for Heisenberg spin chains

Pozsgay¹

2013

J. Stat. Mech.

140

201

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We consider the Generalized Gibbs Ensemble (GGE) in the context of global quantum quenches in XXZ Heisenberg spin chains. Embedding the GGE into the Quantum Transfer Matrix formalism we develop an iterative procedure to fix the Lagrange-multipliers and to calculate predictions for the long-time limit of short-range correlators. The main idea is to consider truncated GGE's with only a finite number of charges and to investigate the convergence of the numerical results as the truncation level is increased. As an example we consider a quantum quench situation where the system is initially prepared in the Néel state and then evolves with an XXZ Hamiltonian with anisotropy ∆ > 1. We provide predictions for short range correlators and gather numerical evidence that the iterative procedure indeed converges. The results show that the system retains memory of the initial condition, and there are clear differences between the numerical values of the correlators as calculated from the purely thermal and the Generalized Gibbs ensembles.

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Computation of Static Heisenberg-Chain Correlators: Control over Length and Temperature Dependence

Cited by 50 publications

References 22 publications

Current operators in integrable spin chains: lessons from long range deformations

Current operators in integrable spin chains: lessons from long range deformations

The equilibrium landscape of the Heisenberg spin chain

The generalized Gibbs ensemble for Heisenberg spin chains

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