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arXiv:2410.13354 · Physical review. B./Physical review. B

Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry

Urei Miura, Keisuke Totsuka

Published Feb 18, 2025• 2 citations
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Abstract

We investigate the emergence of spacetime supersymmetry (SUSY) in an interacting Kitaev chain model with explicit microscopic $\mathcal{N}=1$ quantum mechanical SUSY. As the interaction strength is varied, the model transitions from a weak-coupling gapless phase with spontaneously broken SUSY to a strong-coupling phase with restored SUSY. In this paper, we numerically determine the transition point and investigate the phase structure around it. The weak-coupling phase is governed by the Ising conformal field theory (CFT) with central charge $c=1/2$, which agrees with the prediction made in our previous paper. At the SUSY restoration transition, which borders the strong-coupling gapped phase, the transition belongs to the $c=7/10$ tricritical Ising universality with emergent superconformal invariance. Crucially, the phase structure around the transition closely aligns with the scenario proposed by Zamolodchikov and others based on the integrable deformation of CFTs. These findings provide a concrete example of a lattice model where explicit microscopic supersymmetry at criticality enriches the understanding of phase transitions governed by supersymmetric conformal field theories.

DOI
10.1103/physrevb.111.075136

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We investigate the emergence of spacetime supersymmetry (SUSY) in an interacting Kitaev chain model with explicit microscopic N=1\mathcal{N}=1N=1 quantum mechanical SUSY. As the interaction strength is varied, the model transitions from a weak-coupling gapless phase with spontaneously broken SUSY to a strong-coupling phase with restored SUSY. In this paper, we numerically determine the transition point and investigate the phase structure around it. The weak-coupling phase is governed by the Ising conformal field theory (CFT) with central charge c=1/2c=1/2c=1/2, which agrees with the prediction made in our previous paper. At the SUSY restoration transition, which borders the strong-coupling gapped phase, the transition belongs to the c=7/10c=7/10c=7/10 tricritical Ising universality with emergent superconformal invariance. Crucially, the phase structure around the transition closely aligns with the scenario proposed by Zamolodchikov and others based on the integrable deformation of CFTs. These findings provide a concrete example of a lattice model where explicit microscopic supersymmetry at criticality enriches the understanding of phase transitions governed by supersymmetric conformal field theories.
While experimental evidence for spacetime supersymmetry (SUSY) in particle physics remains elusive, condensed matter systems offer a promising arena for its emergence at quantum critical points (QCPs). Although there have been a variety of proposals for emergent SUSY at symmetry-breaking QCPs, the emergence of SUSY at fractionalized QCPs remains largely unexplored. Here, we demonstrate emergent spacetime SUSY at a fractionalized QCP in the Kitaev honeycomb model with Su-Schrieffer-Heeger (SSH) spin-phonon coupling. Specifically, through numerical computations and analytical analysis, we show that the anisotropic SSH-Kitaev model hosts a fractionalized QCP between a Dirac spin liquid and an incommensurate or commensurate valence-bond-solid phase coexisting with Z_{2} topological order. A low-energy field theory incorporating phonon quantum fluctuations reveals that this fractionalized QCP features an emergent N=2 spacetime SUSY. We further discuss their universal experimental signatures in thermal transport and viscosity, highlighting the concrete lattice realization of emergent SUSY at a fractionalized QCP in 2D.
We introduce and study a lattice fermion model in one dimension with explicit N=1\mathcal{N}=1N=1 supersymmetry (SUSY). The Hamiltonian of the model is defined by the square of a supercharge built from Majorana fermion operators. The model describes interacting Majorana fermions, and its properties depend only on a single parameter ggg. When g=1g=1g=1, we find that SUSY is unbroken and the ground states are identical to those of the frustration-free Kitaev chains. We also find a parameter regime in which SUSY is restored in the infinite-volume limit. For sufficiently large ggg, we prove that SUSY is spontaneously broken and the low-lying excitations are gapless, which can be thought of as Nambu-Goldstone fermions. We then show numerically that these gapless modes have cubic dispersion at long wavelengths.
Majorana fermions have been an important subject of research for the past few years in the field of condensed matter physics. After the realization of Majorana zero mode (MZM) in a Kitaev-chain, studies on the systems of many-body MZMs have been increased. Throughout the previous research, It was found that a few of the Majorana zero mode 1-dimensional chain models possess a Tricritical Ising model conformal field theory as a critical point in their phase diagram. These critical points are supersymmetric and the supersymmetric behaviour remains at a near vicinity of them in their neighbouring gapped phase. This particular behaviour of these 1D strongly-interacting MZMs is believed to be interesting since the system possesses a supersymmetric phase whilst having a nite correlation length in the gapped phase. In this thesis, we are going to investigate the supersymmetric realization of these models in their gapped phase, try to understand their excitation levels with the concept of soliton/antisoliton states and try to find traces of supersymmetry in this system of a condensed matter.
A strongly interacting chain of Majorana fermions realizes the supersymmetric tricritical Ising phase, with supersymmetry (SUSY) extending into a symmetry-broken ordered phase adjacent to the tricritical point. Although the signatures of SUSY at the tricritical point are well understood, their behavior in the gapped phase remains less clear. Here, we address two key questions: how SUSY manifests in the gapped phase and what is the nature of the excitations in this phase. We show that, in the thermodynamic limit, a conventional SUSY diagnostic that remains finite at the tricritical point diverges immediately on the Ising side, yet decays continuously to zero deeper in the gapped phase, signaling the persistence of SUSY. Focusing on the lowest excited states in the supersymmetric gapped regime, we find that the excitations consist of soliton-antisoliton pairs separating distinct ordered regions. Each soliton binds an emergent localized Majorana mode, and together the pair forms a nonlocal Dirac fermion. The occupation of this Dirac mode distinguishes eigenstates with even and odd fermion parity.
We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.