Arxiv Selection Mar 2019
Mar 1-Mar 7 Zehan Li, Mar 8-Mar 14 Jiansong Pan, Mar 15-Mar 21 Ahmet Keles, Mar 22- Mar 28 Haiping Hu
Mar 26
arXiv:1903.09144 (replaced) [pdf, other]
Emergent topology and symmetry-breaking order in correlated quench dynamics
Long Zhang, Lin Zhang, Ying Hu, Sen Niu, Xiong-Jun Liu
Quenching a quantum system involves three basic ingredients: the initial phase, the post-quench target phase, and the non-equilibrium dynamics which carries the information of the former two. Here we propose to identify both the topology and symmetry-breaking order in a correlated system, the Haldane-Hubbard model, from quantum dynamics induced by quenching an initial magnetic phase to topologically nontrivial regime. The equation of motion for the complex pseudospin dynamics is obtained through the flow equation method, with the pseudospin evolution shown to obey a microscopic Landau-Lifshitz-Gilbert-like equation. We find that with the particle-particle interaction playing crucial roles, the correlated quench dynamics exhibit robust universal behaviors on the so-called band-inversion surfaces (BISs), from which the nontrivial topology and magnetic orders can be extracted. In particular, the topology of the post-quench regime can be characterized by an emergent dynamical topological pattern of quench dynamics on BISs, which is robust against dephasing and heating induced by interactions; the pre-quench symmetry-breaking orders is read out from a universal scaling behavior of the quench dynamics emerging on the BIS. This work shows insights into exploring profound correlation physics with novel topology by quench dynamics.
arXiv:1902.09747 (replaced) [pdf, ps, other]
Imaginary time crystal of thermal quantum matter
Zi Cai, Yizhen huang, W. Vincent Liu
Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening an avenue to finding exotic phases of quantum matter with collective time modulation and correlation. Here we report that a thermally open quantum ensemble manifests in the dual space of imaginary time with crystalline ordering due to a bath-induced retarded interaction. Exact quantum Monte Carlo simulations are performed to show that this imaginary time crystal phase exhibits characteristic ground-state and thermal properties absent in conventional quantum manybody systems, especially the striking temperature-oscillating behavior of its physical observables.
Mar 25
arXiv:1903.09175 [pdf, other]
Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
Fausto Borgonovi, Felix M. Izrailev, Lea F. Santos
Comments: 11 pages, 7 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech)
We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-1/2. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components Npc (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev. E 99, 010101R (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time-dependence. We show that Npc can be formally expressed as the inverse of the sum of all OTOC's for projection operators. While none of the individual projection-OTOC's shows an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the Npc helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.
arXiv:1903.09176 [pdf, other]
Quantum information scrambling after a quantum quench
Vincenzo Alba, Pasquale Calabrese
Comments: 7 pages, 3 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two intervals of fixed length as a function of their distance is a diagnostic tool for scrambling after a quantum quench. We consider both integrable and non-integrable one dimensional systems. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading, predicting, in the scaling limit of large intervals and times, a decay exponent equal to 1/2. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers.
Mar 22
arXiv:1903.09144 [pdf, other]
Emergent topology and symmetry-breaking order in correlated quench dynamics
Long Zhang, Lin Zhang, Ying Hu, Sen Niu, Xiong-Jun Liu
Comments: 6+10 pages; 4+3 figures
Quenching a quantum system involves three basic ingredients: the initial phase, the post-quench target phase, and the non-equilibrium dynamics which carries the information of the former two. Here we propose to identify both the topology and symmetry-breaking order in a correlated system, the Haldane-Hubbard model, from quantum dynamics induced by quenching an initial magnetic phase to topologically nontrivial regime. The equation of motion for the complex pseudospin dynamics is obtained through the flow equation method, with the pseudospin evolution shown to obey a microscopic Landau-Lifshitz-Gilbert-like equation. We find that, with the particle-particle interaction playing crucial roles, the correlated quench dynamics exhibit robust universal behaviors on the band-inversion surfaces (BISs), from which the nontrivial topology and magnetic orders can be extracted. In particular, the topology of the post-quench regime can be characterized by an emergent dynamical topological pattern of quench dynamics on BISs, which is robust against dephasing and heating induced by interactions; The pre-quench symmetry-breaking orders can be read out from a universal scaling behavior of the quench dynamics emerging on the BIS. This work shows insights into exploring profound correlation physics with novel topology by quench dynamics.
Mar 13
arXiv:1903.04876 [pdf, other]
Pre-topological fractional excitations in the two-leg flux ladder
Marcello Calvanese Strinati, Sharmistha Sahoo, Kirill Shtengel, Eran Sela
Comments: 18 pages, 11 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Gases (cond-mat.quant-gas)
Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between this topological regime with the Tao-Thouless thin torus quasi-1D limit. Using the wire-construction approach, we analyze an emergent charge density wave (CDW) signifying the break-down of topological order, and relate its phase shifts to Wilson loop operators. The CDW amplitude decreases exponentially with the torus circumference once its exceeds the transverse correlation length controllable by the inter-wire coupling. By means of numerical simulation based on the matrix product states (MPS) formalism, we explore the extreme quasi-1D limit in a two-leg flux ladder and present a simple recipe for probing fractional charge excitations in the ν=1/2 Laughlin-like state of hard-core bosons. We discuss the possibility of realizing this construction in cold-atom experiments. We also address the implications of our findings to the possibility of producing non-Abelian zero modes. As known from rigorous no-go theorems, topological protection for exotic zero modes such as parafermions cannot exist in 1D fermionic systems and the associated degeneracy cannot be robust. Our theory of the 1D-2D crossover allows to calculate the splitting of the degeneracy, which vanishes exponentially with the number of wires, similarly to the CDW amplitude.
Mar 12
arXiv:1903.04000 [pdf, other]
Deviation from the Fermi-Liquid Transport Behavior in the Vicinity of a Van Hove Singularity
František Herman, Jonathan Buhmann, Mark H Fischer, Manfred Sigrist
Comments: 11 pages, 8 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el)
Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr2RuO4 when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impurity scattering, we clarify the role of the diverging density of states together with the locally flat band at the point of the Lifshitz transition. Additionally including electron-electron scattering numerically, we find good qualitative agreement with resistivity measurements on uni-axially strained Sr2RuO4, including the temperature scaling and the temperature dependence of the resistivity peak. Our results imply that even close to the Lifshitz transition, a description starting from well-defined quasiparticles holds. To test the validity of Boltzmann transport theory near a van Hove singularity, we provide further experimentally accessible parameters, such as thermal transport, the Seebeck coefficient, and Hall resistivity and compare different strain scenarios.
arXiv:1903.04528 [pdf, other]
Dynamical symmetry and breathers in a two-dimensional Bose gas
Raphaël Saint-Jalm, Patricia C.M. Castilho, Édouard Le Cerf, Brice Bakkali-Hassani, Jean-Loup Ville, Sylvain Nascimbene, Jérôme Beugnon, Jean Dalibard
Comments: 9 pages + Appendix + Supplemental Material, 6 figures
Subjects: Quantum Gases (cond-mat.quant-gas)
A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross--Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies and interaction parameters by a scaling transform. Finally we show that some specific initial shapes - uniformly-filled triangles or disks - may lead to a periodic evolution, corresponding to a novel type of breather for the two-dimensional Gross--Pitaevskii equation.
Mar 11
arXiv:1903.03567 [pdf, other]
Quantum valence bond ice theory for proton-driven quantum spin-dipole liquids
Masahiko G. Yamada, Yasuhiro Tada
Comments: 6+3 pages, 3+4 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Materials Science (cond-mat.mtrl-sci); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
We present a theory of a hybrid quantum liquid state, quantum spin-dipole liquid (QSDL), in a hydrogen-bonded electron system, by combining a quantum proton ice and Anderson's resonating valence bond spin liquid, motivated by the recent experimental discovery of a proton-driven QSDL in κ-H3(Cat-EDT-TTF)2 (a.k.a. H-Cat). In our theory, an electron spin liquid and a proton dipole liquid are realized simultaneously in the ground state called quantum valence bond ice, while neither of them can be established independently of the other. Analytical and numerical calculations reveal that this state has a volume-law entanglement entropy between spins and dipoles, which is far beyond the (crude) Born-Oppenheimer approximation. We also examine the stability of QSDL with respect to perturbations and discuss implications for experiments in H-Cat and its deuterated analog D-Cat.
arXiv:1903.03143 (cross-list from hep-th) [pdf, other]
Phases of scrambling in eigenstates
Tarek Anous, Julian Sonner
Comments: 25 pages. 2 figures
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el
We use the monodromy method to compute expectation values of an arbitrary number of light operators in finitely excited ("heavy") eigenstates of holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ threshold, these behave thermally up to small corrections, with an effective temperature determined by the heavy state. Below the threshold we find oscillatory and not decaying behavior. As an application of these results we compute the expectation of the out-of-time order arrangement of four light operators in a heavy eigenstate, i.e. a six-point function. Above the threshold we find maximally scrambling behavior with Lyapunov exponent 2πTeff. Below threshold we find that the eigenstate OTOC shows persistent harmonic oscillations.
arXiv:1903.03716 (cross-list from physics.atom-ph) [pdf, other]
Dimensional effects in Efimov physics
M.T. Yamashita
Subjects: Atomic Physics (physics.atom-ph); Quantum Gases (cond-mat.quant-gas); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)
Efimov physics is drastically affected by the change of spatial dimensions. Efimov states occur in a tridimensional (3D) environment, but disappear in two (2D) and one (1D) dimensions. In this paper, dedicated to the memory of Prof. Faddeev, we will review some recent theoretical advances related to the effect of dimensionality in the Efimov phenomenon considering three-boson systems interacting by a zero-range potential. We will start with a very ideal case with no physical scales, passing to a system with finite energies in the Born-Oppenheimer (BO) approximation and finishing with a general system. The physical reason for the appearance of the Efimov effect is given essentially by two reasons which can be revealed by the BO approximation - the form of the effective potential is proportional to 1/R2 (R is the relative distance between the heavy particles) and its strength is smaller than the critical value given by −(D−2)2/4, where D is the effective dimension.
Mar 8
arXiv:1903.02558 (cross-list from cond-mat.mes-hall) [pdf, other]
Floquet Hopf Insulators
Thomas Schuster, Snir Gazit, Joel E. Moore, Norman Y. Yao
Comments: 6 + 9 pages, 3 + 1 figures
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el)
We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf Z invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet Z2 invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time-evolution, subject to a process in which defects at different quasienergy exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0- or π-quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.
arXiv:1903.02778 [pdf, other]
The multiple symmetry sustaining phase transitions of spin ice
V. Raban, C. T. Suen, L. Berthier, P. C. W. Holdsworth
Comments: 14 pages, 14 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el)
We present the full phase diagram of the dumbbell model of spin ice as a function of temperature, chemical potential and staggered chemical potential which breaks the translational lattice symmetry in favour of charge crystal ordering. We observe a double winged structure with five possible phases, monopole fluid (spin ice), fragmented single monopole crystal phases and double monopole crystal, the zinc blend structure. Our model provides a skeleton for liquid-liquid phase transitions and for the winged structures observed for itinerant magnets under pressure and external field. We relate our results to recent experiments on Ho2Ir2O7 and propose a wide ranging set of new experiments that exploit the phase diagram, including high pressure protocols, dynamical scaling of Kibble-Zurek form and universal violations of the fluctuation-dissipation theorem.
Mar 1
arXiv:1902.06584 (cross-list from cond-mat.str-el) [pdf, ps, other]
Bosonization with background U(1) gauge field
Yuan Yao, Yoshiki Fukusumi
Comments: 9 pages, 8 figures
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Bosonization is one of the most significant frameworks to analyze fermionic systems. In this work, we propose a new bosonization of Dirac fermion coupled with U(1) background gauge field consistent with gauge invariance, global chiral anomaly matching and fermion-boson operator correspondence, either of which is not satisfied by previously developed bosonizations. The bilinear Dirac-mass term condensation paradox and its generalized form are resolved by our bosonization. This new bosonization approach to interacting systems also correctly captures the conformal characters of a significant class of critical lattice models, such as conformal dimensions and conformal anomaly of XXZ spin chain with twisted boundary condition. Our work clarifies the equivalence of fermionic flux insertion and bosonic background charge insertion for two-dimensional conformal field theory
Mar 2
arXiv:1902.09747 [pdf, ps, other]
Imaginary time crystal of quantum gases
Zi Cai, Yizhen huang, W. Vincent Liu
Subjects: Quantum Gases (cond-mat.quant-gas)
Floquet or discrete time crystal was predicted as a form of super-crystallization from the “periodic” time lattice of varying Hamiltonians. Subsequent experiments of trapped ions and nitrogen-vacancy centers discovered it. However, whether such a phase can emerge from time continuum, as originally introduced, remains an open question because of the no-go theorem on quantum mechanical ground state. Here we report that by relaxing the scope to open quantum systems, time crystalline ordering can emerge spontaneously by breaking continuous translational symmetry in imaginary time dual space due to retarded interaction induced by thermal bath. Quantum Monte Carlo simulation is performed to calculate a time order parameter and previously unknown “time” excitation response functions from the Euclidean action.
Mar 5
arXiv:1902.10792 [pdf, other]
Anomalous phase ordering of a quenched ferromagnetic superfluid
L. A. Williamson, P. B. Blakie
Subjects: Quantum Gases (cond-mat.quant-gas)
Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the BerezinskiiKosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as t 1/3 . This second regime of coarsening is associated with a turbulent cascade that transports spin wave energy from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin-waves are noninteracting, the cascade occurs through a dynamic coupling to other degrees of freedom of the system. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices. Our results, which provide a connection between the currently disparate fields of phase ordering dynamics and wave turbulence, offer a paradigm for understanding phase ordering dynamics beyond the current framework built around topological defects.
