Unwinding Fermionic SPT Phases: Supersymmetry Extension

• URL: http://arxiv.org/abs/2011.13921v1
• Date: Fri, 27 Nov 2020 18:59:50 GMT
• Title: Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Authors: Abhishodh Prakash, Juven Wang
• Abstract summary: We show how 1+1-dimensional fermionic symmetry-protected topological states can be protected by supersymmetry. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense. This also means we can uplift and remove certain exotic fermionic anomalies.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity $(-1)^F$, while the anti-unitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., "parity" anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multi-layers of 1+1d Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher spacetime dimensions via a cobordism theory.

Related papers

• Long-range entanglement from spontaneous non-onsite symmetry breaking [3.3754780158324564]
  We show a frustration-free lattice model exhibiting SSB of a non-onsite symmetry. We analytically prove the two-fold ground-state degeneracy and the existence of a finite energy gap. Our work reveals the exotic features of SSB of non-onsite symmetries, which may lie beyond the framework of topological holography.
  arXiv  Detail & Related papers  (2024-11-07T18:59:51Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order [17.38734393793605]
  We propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems.
  arXiv  Detail & Related papers  (2024-10-17T16:36:53Z)
• A Non-Invertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra [0.0]
  We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1d conformal field theory. We use this to determine the universal leading and sub-leading contributions to the non-invertible symmetry-resolved entanglement entropy of a single interval.
  arXiv  Detail & Related papers  (2024-09-04T15:25:05Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Renormalization group and spectra of the generalized P\"oschl-Teller potential [0.0]
  We study the P"oschl-Teller potential $V(x) = alpha2 g_s sinh-2(alpha x) + alpha2 g_c cosh-2(alpha x)$, for every value of the dimensionless parameters $g_s$ and $g_c singularity. We show that supersymmetry of the potential, when present, is also spontaneously broken, along with conformal symmetry.
  arXiv  Detail & Related papers  (2023-08-08T21:44:55Z)
• Entanglement asymmetry in the ordered phase of many-body systems: the Ising Field Theory [0.0]
  Global symmetries of quantum many-body systems can be spontaneously broken. In this study, we examine the entanglement asymmetry of a specific region. We also establish a field theoretic framework in the replica theory using twist operators.
  arXiv  Detail & Related papers  (2023-07-22T17:07:56Z)
• Boundary supersymmetry of 1+1 d fermionic SPT phases [0.0]
  We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian.
  arXiv  Detail & Related papers  (2020-11-24T19:00:21Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.