Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session F37b: Correlations and Topology: Theory and Calculation |
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Sponsoring Units: DCMP Chair: Maxim Dzero, Kent State University Room: 384 |
Tuesday, March 14, 2017 11:15AM - 11:27AM |
F37b.00001: Interaction effects on Mirror symmetry protected topological phases Zi Yang Meng, Chuang Chen, Yuan-Yao He, Xiao Yan Xu, Chen Fang Employing large-scale fermionic quantum Monte Carlo simulations, we investigate the interaction effects on the mirror symmetry protected topological phases. We design a 2D tight-binding model based on honeycomb lattice, where each lattice site has two orbitals with opposite parity. Spin-orbital coupling and inter-orbital hopping terms give rise to nonzero integer mirror Chern number of the noninteracting system. Upon adding electronic interactions, we explore the possibility that the Z-group classification be reduced to a smaller group, i.e., two topologically inequivalent phases in the noninteracting limit can adiabatically evolve into each other in the presence of interaction without symmetry breaking. [Preview Abstract] |
Tuesday, March 14, 2017 11:27AM - 11:39AM |
F37b.00002: Electronic interaction effects on the topological phase of the 1D topological Kondo insulator Jason Pillay, Ian McCulloch The effects of electronic interactions on the topological phase of the one-dimensional topological Kondo insulator is numerically investigated using the matrix-product state density-matrix renormalization group algorithm. We find that the electronic interactions which favors having one electron per site, suppresses electron hopping and thus reduces the effect of the p-wave Kondo coupling. In the presence of the conventional s-wave Kondo coupling, this leads to a topological phase transition from a topological phase into a non-topological phase. [Preview Abstract] |
Tuesday, March 14, 2017 11:39AM - 11:51AM |
F37b.00003: Unconventional Surface Criticality Induced by Quantum Phase Transitions from 2D AKLT Phase to Neel Order Fa Wang, Long Zhang Symmetry-protected topological phases have nontrivial surface states in the presence of certain symmetries, which can either be gapless or be degenerate. In this talk, we will present our studies about the physical consequence of such gapless surface states at the bulk quantum phase transition (QPT) which spontaneously breaks these symmetries. We realize the two-dimensional Affleck-Kennedy-Lieb-Tasaki phase on a square lattice and its QPTs to N\'eel ordered phases by a spin-$\frac{1}{2}$ Heisenberg model on a decorated square lattice. With large-scale quantum Monte Carlo simulations, we find that even though the bulk QPTs are governed by the conventional Landau phase transition theory, the gapless surface states induce unconventional universality classes of the surface critical behaviors. [Preview Abstract] |
Tuesday, March 14, 2017 11:51AM - 12:03PM |
F37b.00004: Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions Xiao Yan Xu, K. S. D. Beach, Kai Sun, F. F. Assaad, Zi Yang Meng Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition. [Preview Abstract] |
Tuesday, March 14, 2017 12:03PM - 12:15PM |
F37b.00005: Quantum Phase transition from $\nu = 1$ Fermionic Integer Quantum Hall phase to $\nu = 1/4$ Bosonic Fractional Quantum Hall phase through Feshbach Resonance Shiuan-Fan Liou, Kun Yang, Zi-Xiang Hu We investigate the quantum phase transition with one species of fermions in $\nu = 1$ fermionic integer quantum Hall phase to $\nu = \frac{1}{4}$ bosonic fractional quantum Hall phase by introducing a p-wave pairing interaction among fermions through Feshbach resonance. Previous theoretical work studying this phase transition through Chern-Simons-Landau-Ginzburg theory showed that this phase transition can be of second order in the (2 + 1)D Ising universality class. Through exact diagonalization method, we demonstrated that it is indeed a second order phase transition. [Preview Abstract] |
Tuesday, March 14, 2017 12:15PM - 12:27PM |
F37b.00006: Quantum Phase Transition from Dirac Semimetal to Quantum Spin-Hall Insulator Yuan-Yao He, Xiao Yan Xu, Kai Sun, Fahker Assaad, Zi Yang Meng, Zhong-Yi Lu Employing determinantal quantum Monte Carlo simulations, we design and investigate a lattice model of fermions coupled with Ising fields. By turning the strength of a transverse field, the Ising spins experience a quantum phase transition from a paramagnetic phase to a ferromagnetic phase, which furthermore triggers a topological phase transition between a Dirac semimetal state and a quantum spin-Hall insulating state for the fermionic degrees of freedom. The nature of such an interaction-driven topological phase transition and the associated quantum critical region are fully revealed by the unbiased numerical approach. [Preview Abstract] |
Tuesday, March 14, 2017 12:27PM - 12:39PM |
F37b.00007: Topological Phase Transitions in Dirac semi-metals of distorted spinels SangEun Han, Gil Young Cho, Eun-Gook Moon We study quantum criticality where a Dirac point breaks into two Weyl points in the presence of instantaneous Coulomb interaction because of breaking time-reversal symmetry. We perform the renormalization group analysis for the low-energy effective theory where the interplay between the Dirac fermion, the order parameter, and Coulomb interaction gives rise an intricate universal dynamics. We find that the ratio of the velocities of the order parameter and Dirac fermion is a universal non-trivial value at the quantum critical point, and the dynamics of the system becomes exceedingly anisotropic as we approach the quantum critical point despite of Coulomb interaction which generically tends to make the system isotropic. We apply our theory to the distorted spinels and the diamond lattice, which support Dirac fermions at the high-symmetry points in Brillouin zone. [Preview Abstract] |
Tuesday, March 14, 2017 12:39PM - 12:51PM |
F37b.00008: Quantum phase transitions between a class of symmetry protected topological states Lokman Tsui, Hong-Chen Jiang, Yuan-Ming Lu, Dung-Hai Lee The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension $d$ and symmetry group $G$ so that the cohomology group, $H^{d+1}(G,U(1))$, contains at least one $Z_{2n}$ or $Z$ factor. We show that the phase transition between the trivial SPT and the root states that generate the $ Z_{2n} $ or $Z$ groups can be induced on the boundary of a d+1 dimensional $G\times Z_2^T$-symmetric SPT by a $Z_2^T$ symmetry breaking field. Moreover we show these boundary phase transitions can be ``transplanted'' to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase. [Preview Abstract] |
Tuesday, March 14, 2017 12:51PM - 1:03PM |
F37b.00009: Anomaly indicators for time-reversal symmetric topological orders Chenjie Wang, Michael Levin Some time-reversal symmetric topological orders are anomalous in that they cannot be realized in strictly two-dimensions without breaking time reversal symmetry; instead, they can only be realized on the surface of certain three-dimensional systems. We propose two quantities, which we call {\it anomaly indicators}, that can detect if a time-reversal symmetric topological order is anomalous in this sense. Both anomaly indicators are expressed in terms of the quantum dimensions, topological spins, and time-reversal properties of the anyons in the given topological order. The first indicator, $\eta_2$, applies to bosonic systems while the second indicator, $\eta_f$, applies to fermionic systems in the DIII class. We conjecture that $\eta_2$, together with a previously known indicator $\eta_1$, can detect the two known $\mathbb Z_2$ anomalies in the bosonic case, while $\eta_f$ can detect the $\mathbb Z_{16}$ anomaly in the fermionic case. [Preview Abstract] |
Tuesday, March 14, 2017 1:03PM - 1:15PM |
F37b.00010: Gauging spatial symmetries and the classification of topological crystalline phases Dominic Else, Ryan Thorngren A \emph{topological crystalline} phase of matter is a topological phase protected by space-group symmetries. The prototypical examples are the so-called ``topological crystalline insulators''. For strongly interacting topological crystalline phases, there is as yet no systematic theory. This is in contrast to the case of \emph{internal} symmetries, where coupling to a background gauge field allows one to derive a systematic classification. In this work, we elucidate what it means to gauge a spatial symmetry, allowing us to give a systematic classification of topological crystalline phases. Our work applies to a subset of topological crystalline phases which we call ``topological crystalline liquids''; we conjecture that this subset includes nearly all topological crystalline phases, with the exception of states with exotic fracton excitations such as the ``Haah code''. As an example, we classify bosonic topological crystalline liquids for all 230 space groups. [Preview Abstract] |
Tuesday, March 14, 2017 1:15PM - 1:27PM |
F37b.00011: The Tenfold Way: Fermionic Systems with $N$-body interactions Vijay B. Shenoy, Adhip Agarwala, Arijit Haldar We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary $N$-body interactions. We identify four types of symmetries that such systems can possess, which consist of one ordinary type (usual unitary symmetries), and three {\em non}-ordinary symmetries (such as time reversal, charge conjugation and sublattice). Focusing on systems that possess no non-trivial ordinary symmetries, we demonstrate that the non-ordinary symmetries are strongly constrained. This approach not only leads very naturally to the tenfold classes, but also obtains the canonical representations of these symmetries in each of the ten classes. We also provide a group cohomological perspective of our results in terms of projective representations. We then use the canonical representations of the symmetries to obtain the structure of Hamiltonians with arbitrary $N$-body interactions in each of the ten classes. We show that the space of $N$-body Hamiltonians has an affine subspace (of a vector space) structure in classes which have either or both charge conjugation and sublattice symmetries. Our results can help address open questions on the topological classification of interacting fermionic systems. [Preview Abstract] |
Tuesday, March 14, 2017 1:27PM - 1:39PM |
F37b.00012: Minimalist approach to the classification of symmetry protected topological phases Zhaoxi Xiong A number of proposals with differing predictions (e.g. group cohomology, cobordisms, group supercohomology, spin cobordisms, etc.) have been made for the classification of symmetry protected topological (SPT) phases. Here we treat various proposals on equal footing and present rigorous, general results that are independent of which proposal is correct. We do so by formulating a minimalist Generalized Cohomology Hypothesis, which is satisfied by existing proposals and captures essential aspects of SPT classification. From this Hypothesis alone, formulas relating classifications in different dimensions and/or protected by different symmetry groups are derived. Our formalism is expected to work for fermionic as well as bosonic phases, Floquet as well as stationary phases, and spatial as well as on-site symmetries. [Preview Abstract] |
Tuesday, March 14, 2017 1:39PM - 1:51PM |
F37b.00013: Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo Zi-Xiang Li, Yi-Fan Jiang, Hong Yao A fundamental open issue in physics is whether and how the fermion-sign-problem in quantum Monte Carlo (QMC) can be avoided generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to avoid the fermion-sign-problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two \textit{fundamental} symmetry classes which are sign-problem-free and which we call ``Majorana-class'' and ``Kramers-class'', respectively. Novel sign-problem-free models in the Majorana-class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly-correlated systems and interacting topological matters.\\\ Ref: Zi-Xiang Li, Yi-Fan Jiang, Hong Yao,arXiv:1601.05780 (accepted by Phys. Rev. Lett.) [Preview Abstract] |
Tuesday, March 14, 2017 1:51PM - 2:03PM |
F37b.00014: Quantum critical point preempted by nematicity Shi-Xin Zhang, Shao-Kai Jian, Hong Yao We explore the nature of the topological phase transitions from double-Weyl semimetals to trivial insulators or 3D Chern insulators, describing the annihilation of two double-Weyl nodes with opposite chiralities. With only short-range interactions, the transition can be a continuous one of Lifshitz type, as expected. However, from renormalization group analysis, we find that this quantum critical point is unstable against (even infinitesimal) long-range Coulomb interactions by emerging intermediate phases with nematic ordering. In other words, with finite (even infinitesimal) long-range Coulomb interactions, the topological quantum critical points are preempted by nematic phases. [Preview Abstract] |
Tuesday, March 14, 2017 2:03PM - 2:15PM |
F37b.00015: Scaling behavior of many-body ground-state overlaps beyond the Anderson orthogonality catastrophe Jiahua Gu, Kai Sun In the thermodynamic limit, a many-body ground state has zero overlap with its slightly perturbed state, known as the Anderson orthogonality catastrophe. The amplitude of the overlap for two generic ground states typically exhibits exponential or power-law decay as the system size increases to infinity. In this talk, we show (with examples) that for two topologically different many-body states, there exists a sub-leading term beyond this scaling behavior. Such a sub-leading scaling behavior could be utilized to distinguish topologically different states or serve as a signature for topological phase transitions. [Preview Abstract] |
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