Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Study of dynamical supersymmetry breaking for the two dimensional lattice Wess-Zumino model

Matteo Beccaria, Gian Fabrizio De Angelis, De Angelis, Massimo Campostrini B, Alessandra Feo

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

A new approach to the study of the transition point in a class of two dimensional Wess-Zumino models is presented. The method is based on the calculation of rigorous lower bounds on the ground state energy density in the infinite lattice limit. Such bounds are useful in the discussion of supersymmetry phase transition. The transition point is then determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.

Related papers

Exploring lattice supersymmetry with variational quantum deflation

David Schaich, Chris Culver

Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource requirements, in particular the $\mathcal N = 1$ Wess--Zumino model in 1+1 dimensions, we are exploring ways quantum computing could be used to study spontaneous supersymmetry breaking. A particularly promising recent development is to apply the variational quantum deflation algorithm, which generalizes the variational quantum eigensolver so as to resolve multiple low-energy states.

arXiv:2410.11514•International Symposium on Lattice Field Theory (LATTICE)•Oct 11, 2024•1 citation

Emergence of supersymmetry at a critical point of a lattice model

Sung-Sik Lee

Supersymmetry is a symmetry between a boson and a fermion. Although there is no apparent supersymmetry in nature, its mathematical consistency and appealing properties have led many people to believe that supersymmetry may exist in nature in the form of a spontaneously broken symmetry. In this paper, we explore an alternative possibility by which supersymmetry is realized in nature, that is, supersymmetry dynamically emerges in the low-energy limit of a nonsupersymmetric condensed matter system. We propose a $(2+1)$-dimensional lattice model which exhibits an emergent space-time supersymmetry at a quantum critical point. It is shown that there is only one relevant perturbation at the supersymmetric critical point in the $ϵ$ expansion and the critical theory is the two copies of the Wess-Zumino theory with four supercharges. Exact critical exponents are predicted.

arXiv:cond-mat/0611658•Physical Review B•Aug 6, 2007•148 citations

Tensor network formulation for two-dimensional lattice $$ \mathcal{N} $$ = 1 Wess-Zumino model

Daisuke Kadoh, Yoshinobu Kuramashi, Y. Nakamura +3 more

Abstract Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice $$ \mathcal{N} $$ N = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.

arXiv:1801.04183•Journal of High Energy Physics•Mar 1, 2018•52 citations

Quantum Computing for the Wess–Zumino Model

Chris Culver, David Schaich

Future quantum computers will enable novel sign-problem-free studies of dynamical phenomena in non-perturbative quantum field theories, including real-time evolution and spontaneous supersymmetry breaking. We are investigating applications of quantum computing to low-dimensional supersymmetric lattice systems that can serve as testbeds for existing and near-future quantum devices. Here we present initial results for the $\mathcal{N} = 1$ Wess--Zumino model in 1+1~dimensions, building on our prior analyses of 0+1-dimensional supersymmetric quantum mechanics. In addition to exploring supersymmetry breaking using the variational quantum eigensolver, we consider the prospects for real-time evolution.

arXiv:2301.02230•International Symposium on Lattice Field Theory (LATTICE)•Feb 3, 2023•1 citation

Simulating the Wess-Zumino Supersymmetry Model in Optical Lattices

Yue Yu, Kun Yang

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

arXiv:1005.1399•Physical Review Letters•Oct 8, 2010•80 citations

Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions

Adam Nahum

We suggest the possibility that the two-dimensional $\mathrm{SU}{(2)}_{k}$ Wess-Zumino-Witten (WZW) theory, which has global $\mathrm{SO}(4)$ symmetry, can be continued to $2+\ensuremath{\epsilon}$ dimensions by enlarging the symmetry to $\mathrm{SO}(4+\ensuremath{\epsilon})$. This is motivated by the three-dimensional sigma model with $\mathrm{SO}(5)$ symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\ensuremath{\epsilon}$ may be fixed by assuming analyticity in $\ensuremath{\epsilon}$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality ${d}_{c}>2$. We suggest that ${d}_{c}<3$ for all $k$, and we compute ${d}_{c}$ in the limit of large $k$. The flows support the conjecture that the deconfined phase transition in $\mathrm{SU}(2)$ magnets is a ``pseudocritical'' point with approximate $\mathrm{SO}(5)$, controlled by a fixed point slightly outside the physical parameter space.

arXiv:1912.13468•Physical review. B./Physical review. B•Nov 30, 2020•80 citations
A new approach to the study of the transition point in a class of two dimensional Wess-Zumino models is presented. The method is based on the calculation of rigorous lower bounds on the ground state energy density in the infinite lattice limit. Such bounds are useful in the discussion of supersymmetry phase transition. The transition point is then determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource requirements, in particular the N=1\mathcal N = 1N=1 Wess--Zumino model in 1+1 dimensions, we are exploring ways quantum computing could be used to study spontaneous supersymmetry breaking. A particularly promising recent development is to apply the variational quantum deflation algorithm, which generalizes the variational quantum eigensolver so as to resolve multiple low-energy states.
Supersymmetry is a symmetry between a boson and a fermion. Although there is no apparent supersymmetry in nature, its mathematical consistency and appealing properties have led many people to believe that supersymmetry may exist in nature in the form of a spontaneously broken symmetry. In this paper, we explore an alternative possibility by which supersymmetry is realized in nature, that is, supersymmetry dynamically emerges in the low-energy limit of a nonsupersymmetric condensed matter system. We propose a (2+1)(2+1)(2+1)-dimensional lattice model which exhibits an emergent space-time supersymmetry at a quantum critical point. It is shown that there is only one relevant perturbation at the supersymmetric critical point in the ϵϵϵ expansion and the critical theory is the two copies of the Wess-Zumino theory with four supercharges. Exact critical exponents are predicted.
Tensor network formulation for two-dimensional lattice N \mathcal{N} N = 1 Wess-Zumino model
Abstract Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice N \mathcal{N} N N = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.
Future quantum computers will enable novel sign-problem-free studies of dynamical phenomena in non-perturbative quantum field theories, including real-time evolution and spontaneous supersymmetry breaking. We are investigating applications of quantum computing to low-dimensional supersymmetric lattice systems that can serve as testbeds for existing and near-future quantum devices. Here we present initial results for the N=1\mathcal{N} = 1N=1 Wess--Zumino model in 1+1~dimensions, building on our prior analyses of 0+1-dimensional supersymmetric quantum mechanics. In addition to exploring supersymmetry breaking using the variational quantum eigensolver, we consider the prospects for real-time evolution.
We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.
We suggest the possibility that the two-dimensional SU(2)k\mathrm{SU}{(2)}_{k}SU(2)k​ Wess-Zumino-Witten (WZW) theory, which has global SO(4)\mathrm{SO}(4)SO(4) symmetry, can be continued to $2+\ensuremath{\epsilon}$ dimensions by enlarging the symmetry to $\mathrm{SO}(4+\ensuremath{\epsilon})$. This is motivated by the three-dimensional sigma model with SO(5)\mathrm{SO}(5)SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\ensuremath{\epsilon}$ may be fixed by assuming analyticity in $\ensuremath{\epsilon}$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality dc>2{d}_{c}>2dc​>2. We suggest that dc<3{d}_{c}<3dc​<3 for all kkk, and we compute dc{d}_{c}dc​ in the limit of large kkk. The flows support the conjecture that the deconfined phase transition in SU(2)\mathrm{SU}(2)SU(2) magnets is a ``pseudocritical'' point with approximate SO(5)\mathrm{SO}(5)SO(5), controlled by a fixed point slightly outside the physical parameter space.