Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session E25: Disorder and Localization in AMO Systems I: Time Crystals, Diffusion, Quantum ChaosFocus

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Sponsoring Units: DAMOP DCMP Chair: Anushya Chandran, Boston University Room: BCEC 160A 
Tuesday, March 5, 2019 8:00AM  8:36AM 
E25.00001: Discrete time crystals in longrange interacting systems Invited Speaker: Norman Yao A generic periodically driven, isolated system will absorb energy until it looks, locally, like an infinitetemperature state. However, when the drive frequency is large compared with the local energy scales of the system, then the system can only absorb energy from the drive by spreading it out over many excitations. Consequently, heating occurs very slowly, and there is a longlived quasisteady state  a socalled "prethermal" state  in which ordered phases of matter can occur. In this context, I will describe how longrange interactions can stabilize prethermal timetranslation symmetry breaking in one dimensional systems (even in the absence of disorder). I will begin by motivating a new definition for lightcones in powerlaw interacting quantum systems and using this definition, I will prove that longrange, prethermal time crystals naturally exhibit exponentially long lifetimes. Finally, an experimental realization of a one dimensional, prethermal time crystal in trapped atomic ions will be discussed. 
Tuesday, March 5, 2019 8:36AM  8:48AM 
E25.00002: NMR observations of discrete time crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate Robert Blum, Jared Rovny, Sean Barrett The discrete time crystal (DTC) is a recentlydescribed phase of driven quantum systems that breaks the discrete time translation symmetry of its drive. If the Hamiltonian has period T, the signature of a DTC is a response of period nT that is robust to "error" in the drive. Two experiments recently reported this signature in trapped ions [1] and in diamond NV centers [2]. We present signatures of DTC order [3,4] in an NMR system of ^{31}P spins in an oriented crystal of ammonium dihydrogen phosphate (ADP), a clean sample with multiple dipolarcoupled spin species (^{1}H, ^{31}P, ^{14}N). By varying the pulse angle θ and delay time τ of the DTC pulse sequence, we observe robust DTC oscillations across a much greater range in (θ, τ) than has been observed in earlier experiments [1,2], both with and without ^{1}H decoupling. 
Tuesday, March 5, 2019 8:48AM  9:00AM 
E25.00003: Beyond discrete time crystal signatures: hidden coherence, causes of decay, and the first ‘discrete time crystal echo’ Jared Rovny, Robert Blum, Sean Barrett The phase structure of driven quantum systems can include exotic phenomena, including the recentlydescribed discrete time crystal (DTC). The key signature of a DTC is a response with period nT (n=2,3,…) for drive period T, even when the drive is imperfect. Two experiments recently demonstrated this signature, one in trapped ions [1], and the other in diamond NV centers [2]. We have shown this signature in an NMR system of ^{31}P spins on a crystal lattice, with little to no disorder [3,4]. We study the decay of the DTC oscillations, with two main results. First, we use a novel “DTC echo” sequence to demonstrate that the decay is caused in part by coherent evolution. Second, we demonstrate that the observed decay for perfect pi pulses (ε = 0) can be produced by the action of the internal Hamiltonian during the pulses. 
Tuesday, March 5, 2019 9:00AM  9:12AM 
E25.00004: SpatialTranslationInduced Discrete Time Crystals Kaoru Mizuta, Kazuaki Takasan, Masaya Nakagawa, Norio Kawakami Time crystals, where time translation symmetry is spontaneously broken, are novel phases of matters in that they are proved to exist only in nonequilibrium[1]. In particular, time crystals in Floquet systems, called discrete time crystals (DTCs), have attracted much interest because of theoretical developments[2] and recent experimental realization[3]. 
Tuesday, March 5, 2019 9:12AM  9:24AM 
E25.00005: Quantum diffusion in the strong tunneling regime Nisarga Paul, Ariel Amir We discuss the dynamics of a quantummechanical wavepacket in a noisy environment (i.e., timedependent disorder), modeled using a tightbinding Hamlitonian. It has been found that the fluctuating environment may give rise to diffusive behavior (rather than Anderson localization, which occurs for timeindependent disorder). We develop a new approach to this problem by considering the dynamics as arising from multiple LandauZener crossing events. We find the conditions for the validity of the approach, and use it to calculate how the diffusion constant depends on the noise. The analytical results are corroborated numerically. The results may be applicable to exciton diffusion in photosynthesis and electronic transport in solidstate physics. 
Tuesday, March 5, 2019 9:24AM  9:36AM 
E25.00006: QuantumSpin Diffusion Driven by Ergodic and NonErgodic Finite Spin Baths Walter Hahn, Viatcheslav Dobrovitski We investigate spin diffusion driven by a finite quantum spin bath in a system accessible for solidstate NMR experiments; namely polycrystalline Lalanine. The direct spin transport within the subsystem consisting of dipolar coupled carbon spins is suppressed due to disorder given by different Larmor frequencies. Spin diffusion is, therefore, governed by the surrounding network of proton spins1/2. This proton network consists of strongly coupled groups which are weakly interacting among each other. By means of numerical simulations, we model realistic solidstate NMR experiments. We show that nearby proton spins govern the local magnetic field for carbon spins, while the farther proton spins determine dynamics within the proton bath. In particular, the farther proton spins provide ergodicity in the proton bath and, thereby, drastically change the spin diffusion in the carbon subsystem. We also consider deuterated alanine with all proton spins1/2 replaced by deuteron spins1. For deuterated Lalanine, we show that the local magnetic fields created by deuterons is insufficient to allow for spin diffusion due to the small magnetic dipole moment of deuterons. Instead, spin diffusion is governed by the spinlattice relaxation of deuteron spins on much larger time scales. 
Tuesday, March 5, 2019 9:36AM  9:48AM 
E25.00007: Signatures of Quantum Chaos in Classically NonChaotic Systems Efim Rozenbaum, Leonid Bunimovich, Victor Galitski One of the original goals in the field of quantum chaos was to establish a correspondence between the dynamics of chaotic classical systems and their quantum counterparts. The general issue is that quantummechanical interference washes out classical chaos after a very short (logarithmic) time, and the correspondence breaks down. Recently, outoftimeordered correlator, a universal tool to study quantum chaos, has received a lot of attention due to its versatility and natural interpretation. We use this diagnostic to show that a new kind of drastic disagreement can occur between quantum and classical counterparts of the same model. Remarkably, quantum mechanics appears capable of playing the opposite to its usual role. In particular, it brings chaos to a family of classically nonchaotic systems, where on the quantum side, we demonstrate the Lyapunovlike exponential growth of OTOC. 
Tuesday, March 5, 2019 9:48AM  10:00AM 
E25.00008: The longestlived current in a quantum chaotic spin chain Arnold K. Mong, David Huse To explore issues of numerically capturing dissipative dynamics in closed manybody quantum systems, we have studied the relaxation of nonconserved current operators in a certain quantum chaotic spin chain. The Hamiltonian is a translationallyinvariant spin1/2 chain with nearestneighbor XY interactions and a tilted field that breaks the conservation of total Z magnetization. We look at an infinite chain and examine the relaxation of all “current” operators that have total momentum zero and are odd under spatial inversion. The relaxation is via operator spreading: a unitary flow in operator space from simple short Pauli strings to long (and thus nonlocal) Pauli strings. To approximate this numerically, we limit the length of the Pauli strings and introduce an artificial nonunitary damping that acts only on the longest Pauli strings that we keep, and solve exactly for the longestlived current operator in this approximation. We find that there is a regime of this artificial damping where we obtain a good approximation to the correct unitary dynamics, while in other regimes the artificial damping causes a blockage of the proper unitary flow in operator space and, as a result of this “bad plumbing”, gives incorrect results. 
Tuesday, March 5, 2019 10:00AM  10:12AM 
E25.00009: Quantum Chaos for the Unitary Fermi Gas from the Generalized Boltzmann Equations Pengfei Zhang we study the chaotic behavior of the unitary Fermi gas in both high and low temperature limits by calculating the Quantum Lyapunov exponent defined in terms of the outoftimeorder correlator. We take the method of generalized Boltzmann equations derived from the augmented Keldysh approach. At high temperature, the system is described by weakly interacting fermions with two spin components and in the low temperature limit, the system is a superfluid and can be described by phonon modes. By comparing these to existing results of heat conductivity, we find that D\ll v^2 \tau_L. We argue that this is related to conservation laws for such systems with quasiparticles. 
Tuesday, March 5, 2019 10:12AM  10:24AM 
E25.00010: Chaos and integrability in experimentally accessible alltoall spin models Gregory Bentsen, Thomas Scaffidi, Vir Bulchandani, IonutDragos Potirniche, Monika SchleierSmith, Ehud Altman In recent years, models of disordered fermions with random, alltoall couplings have emerged as prime candidates for studying the limit of strong chaos in quantum mechanical systems. However, such models are prohibitively difficult to realize experimentally. By contrast, spin models with random, alltoall couplings can be engineered in the context of cavity QED and could provide an opportunity to probe strongly interacting, disordered physics in the laboratory. We show that the class of models most naturally realized in this system has the unusual property of possessing two integrable points in its phase diagram. We construct the integrals of motion explicitly and propose a method to directly measure their characteristics in the experiment. This scheme raises the possibility of tuning the system between classical and quantum physics on the one hand, by varying the effective spin per site, and between integrable and chaotic physics on the other, by varying the effective cavity interactions. 
Tuesday, March 5, 2019 10:24AM  10:36AM 
E25.00011: Scrambling in the Dicke model Yahya Alavirad, Seyed Ali Hosseini Lavasani The scrambling rate $\lambda_L$ associated with the exponential growth of outoftimeordered correlators can be used to characterize quantum chaos. Here we use the Majorana Fermion representation of spin $1/2$ systems to study quantum chaos in the Dicke model. We take the system to be in thermal equilibrium and compute $\lambda_L$ throughout the phase diagram to leading order in $1/N$. We find that the chaotic behavior is strongest close to the critical point. At high temperatures $\lambda_L$ is nonzero over an extended region that includes both the normal and superradiant phases. At low temperatures $\lambda_L$ is nonzero in (a) close vicinity of the critical point and (b) a region within the superradiant phase. In the process we also derive a new effective theory for the superradiant phase at finite temperatures. Our formalism does not rely on the assumption of total spin conservation. 
Tuesday, March 5, 2019 10:36AM  10:48AM 
E25.00012: Quantum inverse freezing and mirrorglass order Thomas Iadecola, Michael Schecter It is well known that spontaneous symmetry breaking in one spatial dimension is thermodynamically forbidden at finite energy density. Here we show that mirrorsymmetric disorder in an interacting quantum system can invert this paradigm, yielding spontaneous breaking of mirror symmetry only at finite energy density and giving rise to “mirrorglass” order. The mirrorglass transition, which occurs via the energetic activation of a finite density of emergent Ising degrees of freedom, is enabled by manybody localization and appears to occur simultaneously with the localization transition. This counterintuitive manifestation of localizationprotected order can be viewed as a quantum analog of inverse freezing, a phenomenon that occurs, e.g., in certain models of classical spin glasses. 
Tuesday, March 5, 2019 10:48AM  11:00AM 
E25.00013: Out of Time Ordered Correlators in the Random Field XX Spin Chain Jonathon Riddell, Erik Sorensen We study out of time order correlations, C(x,t) and entanglement growth in the random field XX model with open boundary conditions using the exact JordanWigner transformation to a fermionic Hamiltonian. For any nonzero strength of the random field this model describes an Anderson insulator. Two scenarios are considered: A global quench with the initial state corresponding to a product state of the Néel form, and the behaviour in a typical thermal state at β=1. As a result of the presence of disorder the information spreading as described by the out of time correlations stops beyond a typical length scale, 
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