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arXiv:2403.19601

Topological Phases and Phase Transitions with Dipolar Symmetry Breaking

Amogh Anakru, Zhen Bi

Published Mar 28, 2024• 0 citations
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Abstract

Systems with dipole moment conservation have been of recent interest, as they realize both novel quantum dynamics and exotic ground state phases. In this work, we study some generic properties of 1-D and 2-D dipole-conserving fermionic models at integer fillings. We find that a dipolar symmetry-breaking phase can result in a mean-field band insulator whose topological indices can strongly affect the low-energy physics of the dipolar Goldstone modes. We study the 2-D topological phase transition of the mean-field ground states in the presence of the Goldstone modes. The critical theory resembles the 2+1d quantum electrodynamics coupled to massless Dirac fermions with some crucial differences and shows a novel quantum critical point featuring a nontrivial dynamical exponent. We also discuss the analogous case of 1-D dipole-conserving models and the role of topological invariants.

DOI
10.48550/arxiv.2403.19601

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Systems with dipole moment conservation have been of recent interest, as they realize both novel quantum dynamics and exotic ground state phases. In this work, we study some generic properties of 1-D and 2-D dipole-conserving fermionic models at integer fillings. We find that a dipolar symmetry-breaking phase can result in a mean-field band insulator whose topological indices can strongly affect the low-energy physics of the dipolar Goldstone modes. We study the 2-D topological phase transition of the mean-field ground states in the presence of the Goldstone modes. The critical theory resembles the 2+1d quantum electrodynamics coupled to massless Dirac fermions with some crucial differences and shows a novel quantum critical point featuring a nontrivial dynamical exponent. We also discuss the analogous case of 1-D dipole-conserving models and the role of topological invariants.
The emergence of fractonic topological phases and novel universality classes for quantum dynamics highlights the importance of dipolar symmetry in condensed matter systems. In this work, we study the properties of symmetry-breaking phases of the dipolar symmetries in fermionic models in various spatial dimensions. In such systems, fermions obtain energy dispersion through dipole condensation. Due to the nontrivial commutation between the translation symmetry and dipolar symmetry, the Goldstone modes of the dipolar condensate are strongly coupled to the dispersive fermions and naturally give rise to non-Fermi liquids at low energies. The infrared description of the dipolar symmetry-breaking phase is analogous to the well-known theory of a Fermi surface coupled to an emergent U(1) gauge field. We also discuss the crossover behavior when the dipolar symmetry is slightly broken and the cases with anisotropic dipolar conservation.
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This thesis focuses on the effects of strong electron-electron interactions on topological phase transitions.In very general terms, topological phase transitions are typically associated with the formation of gapless states at the boundary between two gapped phases.The opening of a gap is usually associated with a spontaneous symmetry breaking that can obliterate the topological nature of the system.In this work we highlight a completely different destiny for a topological transition in the presence of interaction and we develop a theoretical framework to address this physics identifying the physical origin for the unconventional scenario.In particular, we show that strong electronic correlation can lead to a gap opening at the topological transition without any symmetry breaking.This turns the topological transition discontinuous, thereby giving rise to a quantum critical point connecting the continuous region with the discontinuous one.This unconventional scenario establishes a surprising connection between a topological transition and quantum criticality.By solving a Bernevig-Hughes-Zhang model supplemented with a local symmetric interaction, we demonstrate that the crucial role of orbital polarization naturally emerges, already at the mean-field level.This local parameter effectively captures the essence of the topological transition, complementing the established evaluation of topological invariants and enabling a Landau-like description.Within this framework, we analyze the interplay between band topology and the dynamical effects of electronic correlations, achieved by developing a non-perturbative method for calculating the effective free energy, the Variational Gaussian Approximation, which is compared with both a simple static mean-field, which is not able to capture any critical behavior for the topological transition and with the accurate Dynamical Mean-Field Theory which provides an important benchmark for the accuracy of the approach.We show indeed that dynamical quantum fluctuations can lead to gap opening without any symmetry breaking.The growth of these quantum effects as the interaction is increased turns indeed the topological transition from continuous to discontinuous.This change of behavior is associated with the presence of massive Dirac fermion at the transition point showing a Gross-Neveu critical behaviour near the quantum critical endpoint.We identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism of mass generation.The theory presented offers a broad scope for extension in various directions, ranging from changing the topological model and modifying the interactions, to incorporating non-local effects, or even applying it to entirely trivial strongly correlated models.
Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band-gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first-order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a reentrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.
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Higher order topological insulators (HOTIs) are a novel form of insulating quantum matter, which are characterized by having gapped boundaries that are separated by gapless corner or hinge states. Recently, it has been proposed that the essential features of a large class of HOTIs are captured by topological multipolar response theories. In this paper, we show that these multipolar responses can be realized in interacting lattice models, which conserve both charge and dipole. In this paper we study several models in both the strongly interacting and mean field limits. In two dimensions we consider a ring-exchange model which exhibits a quadrupole response, and can be tuned to a C4{C}_{4}C4​ symmetric higher order topological phase with half-integer quadrupole moment, as well as half-integer corner charges. We then extend this model to develop an analytic description of adiabatic dipole pumping in an interacting lattice model. The quadrupole moment changes during this pumping process, and if the process is periodic we show the total change in the quadrupole moment is quantized as an integer. We also consider two interacting three-dimensional (3D3\mathrm{D}3D) lattice models with chiral hinge modes. We show that the chiral hinge modes are heralds of a recently proposed ``dipolar Chern-Simons'' response, which is related to the quadrupole response by dimensional reduction. Interestingly, we find that in the mean field limit both the two-dimensional and 3D3\mathrm{D}3D interacting models we consider here are equivalent to known models of noninteracting HOTIs (or boundary obstructed versions). The self-consistent mean field theory treatment provides insight into the connection between free-fermion (mean field) theories having vanishing polarization and interacting models where dipole moments are microscopically conserved.