Thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type

• URL: http://arxiv.org/abs/2408.14444v1
• Date: Mon, 26 Aug 2024 17:36:32 GMT
• Title: Thermodynamics and criticality of supersymmetric spin chains of Haldane-Shastry type
• Authors: Federico Finkel, Artemio González-López,
• Abstract summary: We analyze the thermodynamics and criticality properties of four families of su$(m|n)$ supersymmetric spin chains of Haldane-Shastry (HS) type.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We analyze the thermodynamics and criticality properties of four families of su$(m|n)$ supersymmetric spin chains of Haldane-Shastry (HS) type, related to both the $A_{N-1}$ and the $BC_N$ classical root systems. Using a known formula expressing the thermodynamic free energy per spin of these models in terms of the Perron (largest in modulus) eigenvalue of a suitable inhomogeneous transfer matrix, we prove a general result relating the su$(kp|kq)$ free energy with arbitrary $k=1,2,\dots$ to the su$(p|q)$ free energy. In this way we are able to evaluate the thermodynamic free energy per spin of several infinite families of supersymmetric HS-type chains, and study their thermodynamics. In particular, we show that in all cases the specific heat at constant volume features a single marked Schottky peak, which in some cases can be heuristically explained by approximating the model with a suitable multi-level system with equally spaced energies. We also study the critical behavior of the models under consideration, showing that the low-temperature behavior of their thermodynamic free energy per spin is the same as that of a $(1+1)$-dimensional conformal field theory with central charge $c=m+n/2-1$. However, using a motif-based description of the spectrum we prove that only the three families of su$(1|n)$ chains of type $A_{N-1}$ and the su$(m|n)$ HS chain of $BC_N$ type with $m=1,2,3$ (when the sign $\varepsilon_B$ in the Hamiltonian takes the value $-1$ in the latter case) are truly critical.

Related papers

• A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality [0.0]
  We introduce a novel family of translationally-invariant su$(m|n)$ spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing the existence of a boson-fermion duality characteristic of this type of systems.
  arXiv  Detail & Related papers  (2024-07-18T18:00:20Z)
• Symmetry shapes thermodynamics of macroscopic quantum systems [0.0]
  We show that the entropy of a system can be described in terms of group-theoretical quantities. We apply our technique to generic $N$ identical interacting $d$-level quantum systems.
  arXiv  Detail & Related papers  (2024-02-06T18:13:18Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties [0.0]
  We present any $ell$-state energy eigenvalues and the corresponding normalized wave functions of a mentioned system in a closed form. We calculate the non-relativistic thermodynamic quantities for the potential model in question, and investigate them for a few diatomic molecules.
  arXiv  Detail & Related papers  (2023-04-01T23:22:23Z)
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type [0.0]
  We study the thermodynamics and critical behavior of su($m$) spin chains of Haldane-Shastry type at zero chemical potential. We derive explicit formulas for the energy, entropy and specific heat per spin.
  arXiv  Detail & Related papers  (2022-08-08T09:52:37Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• The open Haldane-Shastry chain: thermodynamics and criticality [0.0]
  We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type. We identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities.
  arXiv  Detail & Related papers  (2022-06-06T14:41:06Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.