Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session R37b: Quantum Phase Transitions: Theory and Computation |
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Sponsoring Units: DCMP Chair: Rebecca Flint, Iowa State University Room: 384 |
Thursday, March 16, 2017 8:00AM - 8:12AM |
R37b.00001: Monte Carlo methods in continuous time for lattice Hamiltonians Emilie Huffman, Shailesh Chandrasekharan We show that solutions to fermion sign problems in the CT-INT formulation can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the worldline representation of quantum spins. Combining the idea with meron-cluster methods, we are able to extend the solvable models even further. We demonstrate these novel solutions to sign problems by considering several examples of strongly correlated systems. [Preview Abstract] |
Thursday, March 16, 2017 8:12AM - 8:24AM |
R37b.00002: Investigating Quantum Phase Transitions in Spin-2 AKLT Systems with Tensor Networks Nicholas Pomata, Ching-Yu Huang, Tzu-Chieh Wei The spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the square lattice, a valence-bond solid (VBS) state, has nontrivial symmetry-protected topological order when translation and rotation invariance are imposed. Niggemann, Kl\"{u}mper, and Zittartz previously studied a two-parameter deformation of this state from the AKLT point, which exhibits a second-order phase transition from a disordered VBS phase to a Neel-ordered phase. We re-examine the deformed AKLT model using tensor renormalization methods. In addition to recovering the VBS-Neel transition, we find new transitions into XY-like and product-state phases, which we can characterize using local order parameters and modular matrices. [Preview Abstract] |
Thursday, March 16, 2017 8:24AM - 8:36AM |
R37b.00003: Deconfined criticality in the presence of SO($N$) anisotropy Jonathan D'Emidio, Ribhu K. Kaul SO($N$) quantum magnets have a rich phase diagram that hosts spin-nematic order, valence bond solid order, and spin liquid behavior. The models can also be continuously connected to well studied models of SU($N$) magnets that display deconfined quantum criticality. We investigate the influence of the deconfined critical point on the nearby phase diagram with SO($N$) anisotropy added. [Preview Abstract] |
Thursday, March 16, 2017 8:36AM - 8:48AM |
R37b.00004: Universal corner contributions to Renyi entanglement entropies in 3+1 dimensions Lauren Hayward Sierens, Pablo Bueno, Rajiv Singh, Robert Myers, Roger Melko A vast number of quantum systems in their ground states are known to yield entanglement entropies that scale according to a leading area law. There can be subleading corrections to this area law behaviour, and for critical systems such corrections can potentially contain universal numbers. We perform numerical calculations of Renyi entanglement entropies for massless free bosonic field theories on a lattice in 3+1 dimensions. We focus on the case where the entangled regions are separated by a boundary with a sharp corner and utilize techniques from the numerical linked cluster expansion to isolate the contribution to the Renyi entropy due to the corner. As a result, we uncover new universal numbers corresponding to the underlying low-energy theories that describe the critical behaviour. [Preview Abstract] |
Thursday, March 16, 2017 8:48AM - 9:00AM |
R37b.00005: Universal entanglement scaling at interacting critical points in 2+1. Bohdan Kulchytskyy, Roger Melko Entanglement entropy has emerged as new a paradigm for the study and characterization of condensed matter systems. The scaling of entropy with the size of the entangled region can reveal universal features of the continuum theory which underlies a lattice model. We perform large-scale Monte-Carlo simulations of a 2+1 Ising model tuned to its critical temperature, belonging to the universality class of the Wilson-Fisher fixed point. We study the universal shape-dependent contribution to the entanglement entropy between two complementary cylindrical regions. In the thin strip limit, we extract a universal proportionality constant and relate it to the value of the entanglement entropy associated with sharp corners in the entangling surface. [Preview Abstract] |
Thursday, March 16, 2017 9:00AM - 9:12AM |
R37b.00006: Time-Translation Symmetry Breaking and Reentrant First Order Transition in Periodically Driven Quantum Oscillators Jennifer Gosner, Yaxing Zhang, Bjoern Kubala, Joachim Ankerhold, Mark Dykman Breaking of discrete time-translation symmetry is a well-known phenomenon in dissipative periodically driven systems. An example is a parametric oscillator that displays period doubling when the drive frequency is close to twice the eigenfrequency. Here we show that this phenomenon also occurs in a quantum coherent regime. It emerges when there cross Floquet eigenvalues that differ by a simple fraction of the driving frequency. Specific examples are provided by a nonlinear quantum oscillator driven close to two or three times its eigenfrequency. In both cases multiple crossings occur with the varying parameters of the driving field. Physically, they result from the interference of the Floquet wave functions in the classically inaccessible region. For driving close to three times the eigenfrequency, we find that, a dissipative oscillator supports three states of period-three vibrations that co-exist with the state of no vibrations. The detuning controlls a reentrant kinetic transition, where the state populations change exponentially strongly. We study the rates of switching between the stable states and their peculiar scaling behavior near bifurcation points. The results allow revealing 'time crystals' in simple quantum systems, including the systems studied in circuit QED. [Preview Abstract] |
Thursday, March 16, 2017 9:12AM - 9:24AM |
R37b.00007: Emergence of supersymmetric quantum electrodynamics Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, Hong Yao Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator (TI) hosting three Dirac cones, such as the topological Kondo insulator SmB$_6$. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to $\mathcal{N}$=2 supersymmetric quantum electrodynamics (SQED) in 2+1D, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine exactly certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point, which may be measured in future experiments. [Preview Abstract] |
Thursday, March 16, 2017 9:24AM - 9:36AM |
R37b.00008: Feynman path integrals over entangled states Chris Hooley, Andrew Green, Jonathan Keeling, Steve Simon We construct a Feynman path integral over a sequence of matrix product states, combining insights from field theory and tensor networks. The paths that dominate this path integral include some degree of entanglement. This new feature allows several insights and applications: i. A Ginzburg-Landau description of deconfined phase transitions. ii. The emergence of new classical collective variables in states that are not adiabatically continuous with product states. iii. Features that are captured in product-state field theories by proliferation of instantons are encoded in perturbative fluctuations about entangled saddle points. We briefly describe our general formalism for such path integrals, as well as a couple of simple examples that illustrate their utility. [Preview Abstract] |
Thursday, March 16, 2017 9:36AM - 9:48AM |
R37b.00009: Entanglement entropy of heterogenous system Yuchi He, Roger Mong We calculate the entanglement entropy (EE) between two coupled heterogenous spin chains. The two subsystems could be respectively gapped, conformal critical and Lifshitz critical. In regard of how EE scales with the system length, we investigate when logarithmic law or area law is obeyed. Furthermore, sub-leading term of area law is studied, through which, Lifshitz subsystems distinguish themselves. [Preview Abstract] |
Thursday, March 16, 2017 9:48AM - 10:00AM |
R37b.00010: The twists and flows of entanglement entropy William Witczak-Krempa, Xiao Chen, Thomas Faulkner, Eduardo Fradkin The entanglement entropy (EE) provides new insights into complex quantum states. We study critical theories on tori and cylinders in 2d/3d, focusing on spatial bi-partitions into two cylinders. We allow for twisted boundary conditions along the cycles. Various results are obtained for the universal EE of the relativistic boson and Dirac fermion conformal field theories (CFTs), and for the fermionic quadratic band touching and the boson with z=2 Lifshitz scaling. The shape dependence of the EE clearly distinguishes these theories, although intriguing similarities are found in certain limits. We also study the evolution of the EE when the system is detuned away from its critical point, by employing a renormalized EE. In certain cases we find non-monotonic behavior of the torus EE under RG flow. [Preview Abstract] |
Thursday, March 16, 2017 10:00AM - 10:12AM |
R37b.00011: Dynamic Quantum Phase Transitions in Non-Hermitian Systems Weng-Hang Leong, Ren-Bao Liu Quantum phase transitions are considered in non-Hermitian systems. Quantum criticality occurs at points where the excitation gap closes in the imaginary part. Phase diagrams of 1D anisotropic XY model with complex transverse field are investigated by exact solution. The long-range character of correlation functions would alter dramatically when the system crosses the imaginary zeros of excitation energy at the complex plane of the transverse field. Quantum phase transitions can be obtained not only at the whole gap closing exceptional points, but also at the additional imaginary zero points. In addition, by studying the corresponding 1D p-wave superconductor system with open boundary condition, we find topological phase transitions at the exceptional points. [Preview Abstract] |
Thursday, March 16, 2017 10:12AM - 10:24AM |
R37b.00012: Excited-state quantum phase transitions Lea Santos, Francisco PĂ©rez-Bernal Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. We show how the presence of an ESQPT can be detected also from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for the Lipkin-Meshkov-Glick (LMG) model, which is the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX model. [Preview Abstract] |
Thursday, March 16, 2017 10:24AM - 10:36AM |
R37b.00013: Nonlinear Luttinger Liquid: Exact solution for the Green function from the fourth Painleve transcendent Tom Price, Dmitry Kovrizhin, Austen Lamacraft The linear Luttinger liquid describes many low energy properties of interacting one dimensional quantum systems. A classic example is the quantum Hall edge, where low energy excitations are chiral edge waves, and the electron spectral function is a power law in momentum space. However, the approximation of linear dispersion introduces an exact degeneracy between all states of fixed momentum, so in frequency space the spectral function is a delta peak. To correctly describe the spectral function it is necessary to include electron dispersion. I'll show how the electron Green function including dispersion may be expressed in terms of the fourth Painleve equation, analogous to the celebrated Tracy--Widom distribution that appears in random matrix theory and the Kardar--Parisi--Zhang universality class of stochastic interface growth. [Preview Abstract] |
Thursday, March 16, 2017 10:36AM - 10:48AM |
R37b.00014: The Hall number across a van Hove singularity Ilya Esterlis, Akash Maharaj, Yi Zhang, Brad Ramshaw, Steven Kivelson In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. A non-analytic dependence of $n_H$ on the electron density is universal in the high field limit, but at low fields the behavior is non-singular and non-universal. We find, however, that for suitable choice of band-parameters a singular change in the low-field $n_H$ occurs near a continuous nematic-order-driven Lifshitz transition. This behavior of $n_H$ is similar to that seen in recent experiments in the high temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$, where a sharp drop in $n_H$ occurs below optimal doping. [Preview Abstract] |
Thursday, March 16, 2017 10:48AM - 11:00AM |
R37b.00015: Optimizing laser pulses to control photoinduced electronic states of matter Bin Hwang, Phillip Duxbury Time-resolved angle-resolved photoemission (tr-ARPES) is a challenging experimental method that can provide remarkable insight into the time dependence of electronic states during and after the application of femtosecond laser pulse. We present optimal control theory for photoemission from these light induced states, focusing on phenomena that are well described by tight-binding models. Our optimal control theory will be outlined and used to study a variety of photo-induced states; including negative temperature states, Floquet spectra and topological states. [Preview Abstract] |
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