2017/12/31 by Federico Finkel, F Finkel, Artemio González-López +5
Materials Science · Mathematics · Physics and Astronomy · #Critical phenomena #Criticality #Expression (computer science) #Function (biology) #Non-equilibrium thermodynamics #Organic and Molecular Conductors Research #Partition function (quantum field theory) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Spectrum (functional analysis) #Thermodynamic potential #cond-mat.stat-mech #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1742-5468/aab3f4
published as J. Stat. Mech.-Theory E. (2018) 043101 · 44 pages, 10 figures. Minor corrections, references added
openalex created_date 2018/01/05 · arxiv created 2018/03/15 · openalex publication_date 2018/04/01 · arxiv updated 2018/04/10 · openalex updated_date 2026/08/05
Abstract We study the thermodynamics and critical behavior of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>m</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> supersymmetric spin chains of Haldane–Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldane’s motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mn>1</mml:mn> <mml:mo>⩽</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo>⩽</mml:mo> <mml:mn>2</mml:mn> </mml:mstyle> </mml:math> , determining the critical regions and the corresponding central charge. We also show that in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at T = 0, in contrast with the previously studied <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> case.