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arXiv:1702.08086 · Nuclear Physics B

Finite size and finite temperature studies of the osp(1|2) spin chain

Thiago Silva Tavares, G A P Ribeiro

Published Jun 2, 2017• 2 citations
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Abstract

We studied a quantum spin chain invariant by the superalgebra osp(1|2). We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behavior and we determined its central charge. We also studied the thermodynamical properties of the spin chain via non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing the effective central charge. The computed values are in agreement with the numerical predictions in the literature.

DOI
10.1016/j.nuclphysb.2017.05.020

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We studied a quantum spin chain invariant by the superalgebra osp(1|2). We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behavior and we determined its central charge. We also studied the thermodynamical properties of the spin chain via non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing the effective central charge. The computed values are in agreement with the numerical predictions in the literature.
This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.
We present a novel treatment of finite temperature properties of the onedimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry’s classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the “dressed energy ” formalism established for the analysis of ground state properties.
The supersymmetric tJ model in one dimension is investigated by means of the quantum transfer matrix (QTM). The free energy of the quantum system is given by just the largest eigenvalue of the QTM whereas the next-largest ones determine the correlation lengths at finite temperature. The first step of the analysis consists of an embedding of the QTM into a family of commuting matrices. In the second step the eigenvalues equations are derived by an algebraic Bethe ansatz. Finally, the eigenvalue equations are transformed into a set of nonlinear integral equations. Some numerical results are presented. The specific heat for instance shows the typical Luttinger liquid behavior at low temperatures.