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Open Access Publications from the University of California

Scholarly Works (7 results)

  • Article
  • Peer Reviewed
UC Berkeley Previously Published Works (2023)
In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetry-breaking) orders compete, and are “intertwined” by a Wess-Zumino-Witten (WZW) term, the possibility of spin liquid arises. The resulting spin liquid could have excitations which carry fractional spins and obey non-trivial self/mutual statistics. As a concrete example, we consider the case where the competing orders are the Néel and valence-bond solid (VBS) order on square lattice. Examining different scenarios of vortex condensation from the VBS side, we show that the intermediate phases, including spin liquids, between the Néel and VBS order always break certain symmetry. Remarkably, our starting theory, without fractionalized particles (partons) and gauge field, predicts results agreeing with those derived from a parton theory. This suggests that the missing link between the Ginzberg-Landau-Wilson action of competing order and the physics of spin liquid is the WZW term.
    Cover page: Competing orders, the Wess-Zumino-Witten term, and spin liquidsCreative Commons 'BY' version 4.0 license
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2021)
    In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the SU(2) gauge theory of the π-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.
      Cover page: Non-abelian bosonization in two and three spatial dimensions and applicationsCreative Commons 'BY' version 4.0 license
      • Thesis
      • Peer Reviewed
      UC Berkeley Electronic Theses and Dissertations (2021)

      In this dissertation, we discuss the non-regularizability and the bosonization of massless fermions with relativistic dispersion in 1,2,3 spatial dimensions. The non-regularizability is the root of various quantum anomalies and plays a central role in the physics of symmetry-protected topological phases. We generalized the Nielsen-Ninomiya theorem to all minimal nodal free fermion field theories protected by the time reversal, charge conservation, and charge conjugation symmetries. We prove that these massless field theories cannot be regularized on a lattice while respecting the protection symmetries. However, they can be realized on the boundaries of symmetry-protected topological phases in one higher dimension. We then generalize Witten's non-abelian bosonization of massless free fermion theories in one spatial dimension to two and three spatial dimensions. We shown the resulting boson theories share the same emergent symmetries and anomalies with the fermion theories. Moreover, we also show the boson theories possess fermion degrees of freedom, namely solitons. These bosonized models are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the SU(2) gauge theory of the Mott insulating phase of nearest-neighbor hopping Hubbard model, ``bipartite-Mott insulators'' in 1,2,3 spatial dimensions and twisted bilayer graphene.

        Cover page: Regularizability and bosonization of relativistic massless fermion
        • Article
        • Peer Reviewed
        UC Berkeley Previously Published Works (2020)
        The non-regularizability of free fermion field theories, which is the root of various quantum anomalies, plays a central role in particle physics and modern condensed matter physics. In this paper, we generalize the Nielsen-Ninomiya theorem to all minimal nodal free fermion field theories protected by the time reversal, charge conservation, and charge conjugation symmetries. We prove that these massless field theories cannot be regularized on a lattice.
          Cover page: The “non-regularizability” of gapless free fermion Hamiltonian protected by on-site symmetries
          • Article
          • Peer Reviewed
          UC Berkeley Previously Published Works (2022)
          In this Letter we discuss the classical three-dimensional XY model whose nearest-neighbor interaction is a mixture of cos(θi-θj) (ferromagnetic) and cos2(θi-θj) (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a noncompact U(1) gauge field, the half-integer vortices interact with an extra interaction mediated by a Z2 gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the 't Hooft loops, and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.
            Cover page: Fractional vortices, Z2 gauge theory, and the confinement-deconfinement transitionCreative Commons 'BY-NC' version 4.0 license
            • Article
            • Peer Reviewed
            UC Berkeley Previously Published Works (2019)
            In an earlier work [1] we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension d, the critical states of fermionic SPT phase transitions has an emergent Z2T symmetry and can be realized on the boundary of a d+1-dimensional bulk SPT with an extra Z2T symmetry.
              Cover page: A holographic theory for the phase transitions between fermionic symmetry-protected topological states
              • Article
              • Peer Reviewed
              UC Berkeley Previously Published Works (2017)
              The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Zn×Zn. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.
                Cover page: The phase transitions between Zn×Zn bosonic topological phases in 1+1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases
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