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arXiv:2005.08996 · Physical review. B./Physical review. B

Topological terms on topological defects: A quantum Monte Carlo study

Toshihiro Sato, Martin Hohenadler, Tarun Grover, John McGreevy, Fakher F. Assaad

Published Oct 6, 2021• 9 citations
arXivHTMLPDF

Abstract

Dirac fermions in (2 + 1) dimensions with dynamically generated anticommuting SO(3) antiferromagnetic and ${\mathrm{Z}}_{2}$ Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\ensuremath{\theta}$ term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\ensuremath{\theta}$ term implies that a domain wall of the ${\mathrm{Z}}_{2}$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a (1 + 1)-dimensional SO(3) nonlinear sigma model with $\ensuremath{\theta}$ term at $\ensuremath{\theta}=\ensuremath{\pi}$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the ${\mathrm{Z}}_{2}$ topological defect. Surprisingly, the consequences of the topological term are seen far from the critical point such that the physics of apparently unrelated model systems are naturally understood by invoking them. This concept can be generalized to higher dimensions where (2 + 1)-dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.

DOI
10.1103/physrevb.104.l161105

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Dirac fermions in (2 + 1) dimensions with dynamically generated anticommuting SO(3) antiferromagnetic and Z2{\mathrm{Z}}_{2}Z2​ Kekul'e valence-bond solid (KVBS) masses map onto a field theory with a topological \ensuremathθ\ensuremath{\theta}\ensuremathθ term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The \ensuremathθ\ensuremath{\theta}\ensuremathθ term implies that a domain wall of the Z2{\mathrm{Z}}_{2}Z2​ KVBS order parameter harbors a spin-1/21/21/2 Heisenberg chain, as described by a (1 + 1)-dimensional SO(3) nonlinear sigma model with \ensuremathθ\ensuremath{\theta}\ensuremathθ term at \ensuremathθ=\ensuremathπ\ensuremath{\theta}=\ensuremath{\pi}\ensuremathθ=\ensuremathπ. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-1/21/21/2 chain at the Z2{\mathrm{Z}}_{2}Z2​ topological defect. Surprisingly, the consequences of the topological term are seen far from the critical point such that the physics of apparently unrelated model systems are naturally understood by invoking them. This concept can be generalized to higher dimensions where (2 + 1)-dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.
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We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
In this thesis we will study recent examples of exotic, topological, and many body localized quantum phase transitions. In Chapter 2 we study the quantum phase transition between the Z_2 spin liquid and valence bond solid (VBS) orders on a triangular lattice. We find a possible nematic Z_2 spin liquid intermediate phase and predict a continuous 3d XY* transition to the neighboring columnar and resonating-plaquette VBS phases. In Chapter 3 we demonstrate that an extended Kane-Mele Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin S^z conservation and the previously mentioned strongly interacting fully gapped phase. We argue that the first quantum phase transition is related to the Z_16 classification of the topological superconductor ^3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O(4) nonlinear sigma model field theory with a Theta-term. In Chapter 4 we propose that if the highest and lowest energy eigenstates of a Hamiltonian belong to different SPT phases, then this Hamiltonian can't be fully many body localized. In Chapter 5 we study the disordered XYZ spin chain and its marginally many body localized critical lines, which we find to be characterized by an effective central charge c'=ln2 and continuously varying critical exponents.
We consider a model of Dirac fermions in 2+1 dimensions with dynamically generated, anticommuting SO(3) Néel and Z_{2} Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z_{3} vortices in the Kekulé mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which the Néel, Kekulé, and semimetallic phases meet. The present sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.