The equilibrium landscape of the Heisenberg spin chain

Ilievski, Enej; Quinn, Eoin

doi:10.21468/SciPostPhys.7.3.033

SciPost Physics

The equilibrium landscape of the Heisenberg spin chain

Enej Ilievski, Eoin Quinn

SciPost Phys. 7, 033 (2019) · published 13 September 2019

doi: 10.21468/SciPostPhys.7.3.033
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.3.033
TI  - The equilibrium landscape of the Heisenberg spin chain
PY  - 2019/09/13
UR  - https://scipost.org/SciPostPhys.7.3.033
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 3
SP  - 033
A1  - Ilievski, Enej
AU  - Quinn, Eoin
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.7.3.033,
	title={{The equilibrium landscape of the Heisenberg spin chain}},
	author={Enej Ilievski and Eoin Quinn},
	journal={SciPost Phys.},
	volume={7},
	pages={033},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.3.033},
	url={https://scipost.org/10.21468/SciPostPhys.7.3.033},
}

Cited by 9

Ontology / Topics

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Bethe Ansatz Heisenberg spin chains Transfer matrix

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¹ Enej Ilievski,
² Eoin Quinn

Funders for the research work leading to this publication