Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session V44: Theory of Topological Protection and Related Issues in Correlated Electron Materials |
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Sponsoring Units: DCMP Chair: Efstratios Manousakis, Florida State Univ Room: LACC 504 |
Thursday, March 8, 2018 2:30PM - 2:42PM |
V44.00001: Partial transpose and entanglement negativity in fermionic systems Hassan Shapourian , Ken Shiozaki , Shinsei Ryu The partial transpose of density matrices in many-body systems has been recognized as an important tool to diagnose quantum entanglement of mixed states. In particular, it can be used to define the (logarithmic) entanglement negativity for bosonic systems. In this talk, we introduce partial time-reversal transformation as an analog of partial transpose for fermions. Our definition naturally arises from the spacetime picture of partially transposed density matrices in which partial transpose is equivalent to reversing the arrow of time for one subsystem relative to the other subsystem. We show the success of this definition in capturing the entanglement of fermionic symmetry-protected topological phases as well as conformal field theories in (1+1) dimensions. |
Thursday, March 8, 2018 2:42PM - 2:54PM |
V44.00002: Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries Alex Turzillo , Minyoung You We extend the formalism of Matrix Product States (MPS) to describe one-dimensional gapped systems of fermions with both unitary and anti-unitary symmetries. Additionally, systems with orientation-reversing spatial symmetries are considered. The short-ranged entangled phases of such systems are classified by three invariants, which characterize the projective action of the symmetry on edge states. We give new interpretations of these invariants as properties of states on the closed chain. The relationship between fermionic MPS systems at an RG fixed point and equivariant algebras is exploited to derive a group law for the stacking of fermionic phases. The result generalizes the cobordism classification to symmetry groups that are non-trivial extensions of fermion parity and time-reversal. |
Thursday, March 8, 2018 2:54PM - 3:06PM |
V44.00003: Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging Apoorv Tiwari , Xiao Chen , Ken Shiozaki , Shinsei Ryu We analyze $2+1d$ and $3+1d$ Bosonic Symmetry Protected |
Thursday, March 8, 2018 3:06PM - 3:18PM |
V44.00004: Coupled wire models of surface topological orders for ADE classifications, symmetries and dualities Bo Han , Jeffrey Teo We systematically study 2+1d surface topological orders and their duality and symmetry properties for ADE classes of Lie group theories via coupled wire constructions. We first construct gapped surface topologically ordered systems for ADE classes, by introducing current-current interactions (Gross-Neveu type) on the chiral Luttinger liquid model. We study the property of the ground state and the excitations. Then we perform non-local duality transformations explicitly in terms of the local degrees of freedom on each wire and study properties of the original and dual theories. Most of them are self-dual in the sense that the interactions of both theories have the same form. We also study the symmetry transformation under duality. |
Thursday, March 8, 2018 3:18PM - 3:30PM |
V44.00005: Edge invariant for 3D interacting Floquet systems with translation symmetry Dominic Reiss , Rahul Roy In two dimensions, interacting Floquet topological phases may arise even in the absence of protecting symmetry. These phases are classified by the chiral edge transport at the one dimensional boundary of an open system, which is captured by a chiral unitary index of the effective one dimensional unitary. We study an extension of this index to two dimensional unitaries with translation symmetry. We use this extended index to work towards a classification of 3D interacting topological phases with no symmetry except translation invariance. |
Thursday, March 8, 2018 3:30PM - 3:42PM |
V44.00006: Twisted Fracton Models in Three Dimensions Hao Song , Sheng-Jie Huang , Abhinav Prem , Miguel Angel Martin-Delgado Right now great interests are growing among physicists on a new possibility of quantum phases which support immobile quasiparticles, so-called fractons. Most currently studied fracton models in three dimensions can be viewed as generalized abelian gauge theories. By analogy to Dijkgraaf-Witten topological gauge theories, we notice a simple further generalization of these models by twisting. Based on this observation, we construct a larger family of exactly solvable models, which we dub twisted fracton models. To characterize the corresponding quantum phases, we study their ground state degeneracy under periodic boundary conditions and the topological properties of their quasiparticles. In particular, we see a simple realization of non-abelian fractons. |
Thursday, March 8, 2018 3:42PM - 3:54PM |
V44.00007: Fracton Phase in a Layered Honeycomb Lattice Vijay Shenoy There has been much recent interest in understanding topological phases |
Thursday, March 8, 2018 3:54PM - 4:06PM |
V44.00008: Title: Cage-net condensation: a wave-function picture for discrete fracton phases Sheng-Jie Huang , Abhinav Prem , Hao Song , Michael Hermele In this work, we present a wavefunction approach for studying a large class of fracton phases, which generically support excitations with restricted mobility. We show that a large class of three-dimensional fracton phases can be understood as the condensation of extended objects, dubbed “cage-nets”. These highly fluctuating cage-nets provide a simple wave-function picture for understanding a class of discrete fracton states. We also construct two simple exactly solvable models in which the ground state wavefunctions are cage-net condensates. These models support fractons and non-Abelian excitations that can only move in one- or two-dimensions. We further argue that the fractons will not carry any topological degeneracy in the construction employed in this work. |
Thursday, March 8, 2018 4:06PM - 4:18PM |
V44.00009: Dynamics of Kitaev Spin Liquid under A Local Magnetic Field Shuang Liang , Wei Chen We study the response of a gapless Kitaev spin liquid to a local magnetic field perpendicular to the 2D Kitaev lattice. The Kitaev spin liquid is well known to contain fractionalized excitations of flux and matter majorana fermions. A local magnetic field can not only excite a pair of flux and a majorana fermion, it also introduces a dynamics to the flux excitation. The system including the local magnetic field can be described by an interacting resonant level model. In ordinary metal this model can be mapped to a Kondo problem describing conduction electrons scattered by a magnetic impurity. However, unlike in metals, the density of states for matter fermions vanishes at Dirac points in gapless Kitaev spind liquid. This results in a residue entropy of ln2 of the pseudospin defined by bond fermion states in the Kitaev spin liquid at zero temperature, in contrast to the case in ordinary metal, where the entropy of magnetic impurity vanishes at zero T. This indicates that in opposite to the full screening of magnetic impurity in ordinary metals, there is no 'screening' of the pseudospin at all in the Kitaev spin liquid. At the end, a nonperturbative susceptibility of the spin liquid at both low and high magnetic field is obtained and studied. |
Thursday, March 8, 2018 4:18PM - 4:30PM |
V44.00010: Intrinsically interacting symmetry protected phases of fermions Lukasz Fidkowski , Max Metlitski , Ashvin Vishwanath Interactions can profoundly affect the classification of fermionic symmetry protected topological (SPT) phases. In addition to sometimes collapsing the non-interacting classification, they also enable the existence of entirely new, intrinsically interacting phases, not adiabatically connected to any free fermion topological insulator or superconductor. Beyond the existence of special exactly solved models and an abstract bulk characterization in terms of three loop braiding and cobordism, little is understood about these phases, and in particular about the surface states they admit. In this work, we advance an understanding of the surface states of such intrinsically interacting fermionic SPTs. In particular, we find gapped symmetry preserving topologically ordered surface states, and propose a new ’t Hooft anomaly characterizing such fermionic surfaces, connecting the surface physics to the bulk SPT order. |
Thursday, March 8, 2018 4:30PM - 4:42PM |
V44.00011: Quantum Monte Carlo study of a Z_{2} gauge theory containing phases with and without a Luttinger volume Fermi surface Fakher Assaad , Snir Gazit , Subir Sachdev , Ashvin Vishwanath We describe sign-problem-free quantum Monte Carlo simulations of a model of electrons, c_{α}, at half-filling on the square lattice. The model is a Z_{2 }gauge theory in which the c_{α} are allowed to fractionalize into two partons carrying Z_{2} gauge charges: an `orthogonal’ fermion ψ_{α }carrying both the spin and the electromagnetic charge of the electron, and an Ising matter field. Among the phases found are two with no broken symmetries: (A) an orthogonal semi-metal, which has a Dirac spectrum of the ψ_{α}, and (B) a metal with a Luttinger volume Fermi surface of the c_{α}. |
Thursday, March 8, 2018 4:42PM - 4:54PM |
V44.00012: Bulk-edge correspondence of 1D and 2D periodically driven topological systems Xu Liu , Fenner Harper , Rahul Roy Time-dependent systems have recently been shown to support new types of topological order that are different from the phases in static systems. We find a relationship between the bulk invariant of the unitary evolution of the closed system and the behavior of the edge modes in the open system for one and two dimensional Floquet insulators. For 1D systems with chiral symmetry, we relate the chiral flow at half-period to the number of edge modes in the gaps 0 and π. We also find a bulk-edge correspondence for the different classes of Floquet topological insulators in 2D, and introduce simple models in which these nontrivial topological phases can be realized. |
Thursday, March 8, 2018 4:54PM - 5:06PM |
V44.00013: Finite size scaling of energy in 1D topological system Yuting Wang , Alex Kamenev We investigate the scaling of ground state energy around topological quantum phase transition in one dimension. It is found that the finite-size correction to energy which is uniquely related to its central charge at criticality naturally extends into a scaling function when moving away from the critical point. The scaling function depends only on the ratio of the system size to the correlation length and shows universal behavior among non-interacting and interacting systems. |
Thursday, March 8, 2018 5:06PM - 5:18PM |
V44.00014: Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models Xu Yang , Shenghan Jiang , Ashvin Vishwanath , Ying Ran Lieb-Schultz-Mattis(LSM) theorem and its various generalizations provide a powerful guidance toward the search of novel phases of matter utilizing only information such as filling number and internal/spatial symmetries. Here we propose and prove a modified LSM theorem suitable for 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin (projective symmetry representations) in the unit cell. There are two nontrivial outcomes for gapped ground states that preserve all symmetries. In the first case, one necessarily obtains a symmetry protected topological (SPT) phase with protected edge states. This allows us to readily construct models of SPT states by decorating dimer models to yield SPT phases, which should be useful in their physical realization. In the second case, topological-ordered states are necessarily present. The resulting SPTs for the first case display a dyonic character in that they associate charge with symmetry flux, allowing the flux in the unit cell to screen the projective representation on the sites. We provide an explicit formula that encapsulates this physics, which identifies a specific set of allowed SPT phases. |
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