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arXiv:1806.05656 · Journal of Statistical Mechanics Theory and Experiment

Supersymmetric quantum spherical spins

L G dos Santos, L V T Tavares, P F Bienzobaz, Pedro R S Gomes

Published Dec 1, 2018• 0 citations
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Abstract

Abstract In this work we investigate properties of a supersymmetric extension of the quantum spherical model from an off-shell formulation directly in the superspace. This is convenient to safely handle the constraint structure of the model in a way compatible with supersymmetry. The model is parametrized by an interaction energy, , which governs the interactions between the superfields of different sites. We briefly discuss some consequences when corresponds to the case of first-neighbor interactions. After computing the partition function via saddle point method for a generic interaction, , we focus in the mean-field version, which reveals an interesting critical behavior. In fact, the mean-field supersymmetric model exhibits a quantum phase transition without breaking supersymmetry at zero temperature, as well as a phase transition at finite temperature with broken supersymmetry. We compute critical exponents of the usual magnetization and susceptibility in both cases of zero and finite temperature. Concerning the susceptibility, there are two regimes in the case of finite temperature characterized by distinct critical exponents. The entropy is well behaved at low temperature, vanishing as .

DOI
10.1088/1742-5468/aaf10b

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Abstract In this work we investigate properties of a supersymmetric extension of the quantum spherical model from an off-shell formulation directly in the superspace. This is convenient to safely handle the constraint structure of the model in a way compatible with supersymmetry. The model is parametrized by an interaction energy, , which governs the interactions between the superfields of different sites. We briefly discuss some consequences when corresponds to the case of first-neighbor interactions. After computing the partition function via saddle point method for a generic interaction, , we focus in the mean-field version, which reveals an interesting critical behavior. In fact, the mean-field supersymmetric model exhibits a quantum phase transition without breaking supersymmetry at zero temperature, as well as a phase transition at finite temperature with broken supersymmetry. We compute critical exponents of the usual magnetization and susceptibility in both cases of zero and finite temperature. Concerning the susceptibility, there are two regimes in the case of finite temperature characterized by distinct critical exponents. The entropy is well behaved at low temperature, vanishing as .
Abstract This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.
We use the stochastic quantization method to construct a supersymmetric version of the quantum spherical model. This is based on the equivalence between the Brownian motion described by a Langevin equation and the supersymmetric quantum mechanics, which is connected with the existence of the Nicolai map. We investigate the critical behavior of the supersymmetric model at finite as well as at zero temperatures, showing that it exhibits both classical and quantum phase transitions, and determine the critical dimensions.
We investigate a quantum version of the spherical model which is obtained from the classical Berlin-Kac spherical model by a simple canonical quantization scheme. We find a complete solution of the model for short-range as well as for long-range interactions. At finite temperatures the critical behavior is the same as in the classical spherical model whereas at zero temperature we find a quantum phase transition characterized by new critical exponents. Based on a functional-integral representation of the partition function the free energy of the model is shown to be equivalent to that of the nonlinear \ensuremath{\sigma} model in the limit of infinite order-parameter dimensionality. \textcopyright{} 1996 The American Physical Society.
We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of Becchi-Rouet-Stora-Tyutin supersymmetry. The Ward identities associated with this invariance indicate that the spin glass order parameter must vanish, and as a result the annealed average is exact in this model. We present results for the free energy, entropy, and specific heat. Due to quantum effects, the entropy remains finite and the specific heat vanishes at zero temperature. Results for the phase diagram coincide with those obtained by different formalisms. At zero temperature we derive the scaling behavior with frequency of the dynamical susceptibility.
A mean-field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry breaking. The order parameter function is solved exactly in the whole low temperature phase. The zero-field-cooled susceptibility remains finite at low TTT. Next a quantum version of the system is considered. Whereas the magnetic properties are not altered qualitatively, the thermodynamics is now regular at small temperatures.
Abstract We study the thermodynamics and critical behavior of s u ( m | n ) 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 1 ⩽ m , n ⩽ 2 , determining the critical regions and the corresponding central charge. We also show that in the s u ( 2 | 1 ) , s u ( 1 | 2 ) and s u ( 2 | 2 ) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at T = 0, in contrast with the previously studied s u ( 2 ) case.