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Deconfined quantum criticality with internal supersymmetry

Zhi-Qiang Gao, Hui Yang, Yan-Qi Wang

TL;DR

The paper extends the deconfined quantum critical point (DQCP) paradigm to systems with internal supersymmetry by studying an $OSp(1|2)$-symmetric lattice model that hosts a super-VBS (SVBS) phase and a super-Néel (SN) phase. It develops complementary continuum descriptions: a nonlinear sigma model on the supersphere $S^{4|2}$ with a level-1 WZW term to encode symmetry intertwinement and a SUSY gauge theory that captures the critical dynamics, predicting a route to 3D XY universality. It shows that explicit breaking of the internal SUSY to $SU(2)$ reduces the sDQCP to the conventional DQCP, providing a unified framework for deconfined criticality with or without internal SUSY. The analysis highlights the role of pseudo-Hermiticity and symplectic fermions, and suggests concrete directions for numerical checks and generalizations to other internal supergroups.

Abstract

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg--Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin $SU(2)$, namely $OSp(1|2)$, we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal $OSp(1|2)$ and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including a heuristic argument for 3D XY critical behavior. Finally, we show that explicitly breaking $OSp(1|2)$ down to $SU(2)$ continuously connects our sDQCP to the conventional DQCP scenario.

Deconfined quantum criticality with internal supersymmetry

TL;DR

The paper extends the deconfined quantum critical point (DQCP) paradigm to systems with internal supersymmetry by studying an -symmetric lattice model that hosts a super-VBS (SVBS) phase and a super-Néel (SN) phase. It develops complementary continuum descriptions: a nonlinear sigma model on the supersphere with a level-1 WZW term to encode symmetry intertwinement and a SUSY gauge theory that captures the critical dynamics, predicting a route to 3D XY universality. It shows that explicit breaking of the internal SUSY to reduces the sDQCP to the conventional DQCP, providing a unified framework for deconfined criticality with or without internal SUSY. The analysis highlights the role of pseudo-Hermiticity and symplectic fermions, and suggests concrete directions for numerical checks and generalizations to other internal supergroups.

Abstract

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg--Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin , namely , we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including a heuristic argument for 3D XY critical behavior. Finally, we show that explicitly breaking down to continuously connects our sDQCP to the conventional DQCP scenario.
Paper Structure (9 sections, 21 equations, 1 figure)

This paper contains 9 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The model
  3. The lattice Hamiltonian
  4. The super-VBS phase
  5. The super-Néel phase
  6. Kinetics: Non-linear sigma model formalism
  7. Dynamics: Gauge theory formalism
  8. Explicitly breaking the internal SUSY
  9. Conclusions

Figures (1)

  • Figure 1: Illustration of a VBS (SVBS) vortex. Spin singlets formed by spins on nearest-neighbor bonds are denoted as blue ellipses. The vortex core, which carries spin-$\frac{1}{2}$, is denoted as the red arrow. Around this VBS (SVBS) vortex the four-fold lattice rotation symmetry is locally restored.