arXiv subjects

Alan Morningstar

Publications and source records attributed to Alan Morningstar.

15 recordsLinked to original sources

arXiv2023

Hydrodynamics in long-range interacting systems with center-of-mass conservation

In systems with a conserved density, the additional conservation of the center of mass (dipole moment) has been shown to slow down the associated hydrodynamics. At the same time, long-range interactions generally lead to faster transport and information propagation. Here, we explore the competition of these two effects and develop a hydrodynamic theory for long-range center-of-mass-conserving systems. We demonstrate that these systems can exhibit a rich dynamical phase diagram containing subdiffusive, diffusive, and superdiffusive behaviors, with continuously varying dynamical exponents. We corroborate our theory by studying quantum lattice models whose emergent hydrodynamics exhibit these phenomena.

cond-mat.stat-mech↗

arXiv2023

Many-body resonances in the avalanche instability of many-body localization

Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability towards thermalization of MBL systems is the so-called ``avalanche'', where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.

cond-mat.stat-mech↗

arXiv2022

Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics

Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such systems can undergo dynamical phase transitions in the entanglement properties of quantum trajectories conditional on the measurement outcomes. Here, we explore dynamics in which one attempts to (locally) use those measurement outcomes to steer the system toward a target state, and we study the resulting phase diagram as a function of the measurement and feedback rates. Steering succeeds when the measurement and feedback rates exceed a threshold, yielding an absorbing-state transition in the trajectory-averaged density matrix. We argue that the absorbing-state transition generally occurs at different critical parameters from the entanglement transition in individual trajectories and has distinct critical properties. The efficacy of steering depends on the nature of the target state: in particular, for local dynamics targeting long-range correlated states, steering is necessarily slow and the entanglement and steering transitions are well separated in parameter space.

cond-mat.stat-mech↗

arXiv2022

Universality classes of thermalization for mesoscopic Floquet systems

We identify several phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. We also identify a new Floquet thermal ensemble -- the ladder ensemble -- that is qualitatively distinct from the featureless infinite-temperature state that is often assumed to describe the equilibrium of driven systems. The phases can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order $\omega$ with the drive, i.e., Floquet thermalizes, and (ii) the ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases represent regimes of behavior in mesoscopic systems, but they are sharply defined in a large-system limit where the drive frequency $\omega$ scales up with system size $N$ as the $N\to\infty$ limit is taken: we examine frequency scalings ranging from a weak $\omega \sim \log N$, to stronger scalings ranging from $\omega \sim \sqrt{N}$ to $\omega \sim N$. We show that the transition where Floquet thermalization breaks down occurs at $\omega\sim N$ and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a separation of scales between $N$ and $\omega$. A striking prediction of our work is that, under perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a novel type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems.

cond-mat.stat-mech↗

arXiv2022

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in elucidating fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising synthetic system that combines several advantageous properties. These include a large set of internal states for encoding quantum information, long nuclear and rotational coherence times and long-range, anisotropic interactions. The latter are expected to allow the exploration of intriguing phases of correlated quantum matter, such as topological superfluids, quantum spin liquids, fractional Chern insulators and quantum magnets. Probing correlations in these phases is crucial to understand their microscopic properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy to measure the site-resolved dynamics of quantum correlations in a gas of polar molecules in a two-dimensional optical lattice. Using two rotational states of the molecules, we realize a spin-1/2 system where the particles are coupled via dipolar interactions, producing a quantum spin-exchange model. Starting with the synthetic spin system prepared far from equilibrium, we study the evolution of correlations during the thermalization process for both spatially isotropic and anisotropic interactions. Furthermore, we study the correlation dynamics in a spin-anisotropic Heisenberg model engineered from the native spin-exchange model using Floquet techniques. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states useful for quantum computation and metrology.

cond-mat.quant-gas↗

arXiv2022

Emergence of Fermi's Golden Rule

Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a {\it continuum} of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing; this question arises in a number of recently investigated many-body systems. For different symmetry classes, we analytically and/or numerically calculate the universal crossovers in the average decay of the initial state as the level spacing is varied, with the Golden Rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by FGR is the appearance of the spectral form factor in the long-time regime for small but nonzero level spacing.

quant-ph↗

arXiv2022

Distinct universality classes of diffusive transport from full counting statistics

The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

cond-mat.stat-mech↗

arXiv2021

Simulation of quantum physics with Tensor Processing Units: brute-force computation of ground states and time evolution

Tensor Processing Units (TPUs) were developed by Google exclusively to support large-scale machine learning tasks. TPUs can, however, also be used to accelerate and scale up other computationally demanding tasks. In this paper we repurpose TPUs for the challenging problem of simulating quantum spin systems. Consider a lattice model made of $N$ spin-$\frac{1}{2}$ quantum spins, or qubits, with a Hamiltonian $H = \sum_i h_i$ that is a sum of local terms $h_i$ and a wavefunction $|\Psi\rangle$ consisting of $2^N$ complex amplitudes. We demonstrate the usage of TPUs for both (i) computing the ground state $|\Psi_{gs}\rangle$ of the Hamiltonian $H$, and (ii) simulating the time evolution $|\Psi(t)\rangle=e^{-itH}|\Psi(0)\rangle$ generated by this Hamiltonian starting from some initial state $|\Psi(0)\rangle$. The bottleneck of the above tasks is computing the product $H |\Psi\rangle$, which can be implemented with remarkable efficiency utilising the native capabilities of TPUs. With a TPU v3 pod, with 2048 cores, we simulate wavefunctions $|\Psi\rangle$ of up to $N=38$ qubits. The dedicated matrix multiplication units (MXUs), the high bandwidth memory (HBM) on each core, and the fast inter-core interconnects (ICIs) together provide performance far beyond the capabilities of general purpose processors.

quant-ph↗

arXiv2021

Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization

Tensor Processing Units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks, but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper we demonstrate the usage of TPUs for massively parallel, classical simulations of quantum many-body dynamics on long timescales. We apply our methods to study the phenomenon of Floquet prethermalization, i.e., exponentially slow heating in quantum spin chains subject to high-frequency periodic driving. We simulate the dynamics of L=34 qubits for over $10^5$ Floquet periods, corresponding to circuits with millions of two-qubit gates. The circuits simulated have no additional symmetries and represent a pure-state evolution in the full $2^L$-dimensional Hilbert space. This is achieved by distributing the computation over 128 TPU cores. On that size TPU cluster, we find speedups in wall-clock runtime of 230x and 15x when compared to reference CPU and single-GPU simulations, respectively, for shorter 30-qubit simulations that can be handled by all three platforms. We study the computational cost of the simulations, as a function of both the number of qubits and the number of TPU cores used, up to our maximum capacity of L=40 qubits, which requires a ``full pod" of 2048 TPU cores with tens of terabytes of memory in total. For these simulations, an 8-TPU-core machine is comparable to a single A100 GPU, and thus the full TPU pod is comparable to a machine with hundreds of GPUs. However, the TPU pod is more energy and cost efficient, and readily accessible (via Google Cloud), unlike such large many-GPU configurations. We also study the accumulation of numerical error as a function of circuit depth in very deep circuits. Our work demonstrates that TPUs can offer significant advantages for state-of-the-art simulations of quantum many-body dynamics.

quant-ph↗

arXiv2021

Avalanches and many-body resonances in many-body localized systems

We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some "landmarks" within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).

cond-mat.dis-nn↗

arXiv2020

Many-body localization near the critical point

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $\textit{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \rightarrow \infty$, but the divergence is weaker than for the KT transition.

cond-mat.stat-mech↗

arXiv2020

Kinetically constrained freezing transition in a dipole-conserving system

We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

cond-mat.stat-mech↗

arXiv2019

Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system

Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a "tilt"). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. We study transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength $\lambda$ and tilt strength and find that the associated decay time $\tau$ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with $\tau\propto\lambda^4$. In order to explain the underlying physics we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics.

cond-mat.quant-gas↗

arXiv2019

Renormalization-group study of the many-body localization transition in one dimension

Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built on those of Zhang $\textit{et al.}$ [1] and Goremykina $\textit{et al.}$ [2], which are based on thermal and insulating blocks. Our main addition is to characterize each insulating block with two lengths: a physical length, and an internal decay length $\zeta$ for its effective interactions. In this approach, the MBL phase is governed by a RG fixed line that is parametrized by a global decay length $\tilde{\zeta}$, and the rare large thermal inclusions within the MBL phase have a fractal geometry. As the phase transition is approached from within the MBL phase, $\tilde{\zeta}$ approaches the finite critical value corresponding to the avalanche instability, and the fractal dimension of large thermal inclusions approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG flow, with no intermediate critical MBL phase.

cond-mat.stat-mech↗

arXiv2017

Deep Learning the Ising Model Near Criticality

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural question to ask is whether deep neural networks hold any advantage over shallow networks in representing such data. We investigate this question by using unsupervised, generative graphical models to learn the probability distribution of a two-dimensional Ising system. Deep Boltzmann machines, deep belief networks, and deep restricted Boltzmann networks are trained on thermal spin configurations from this system, and compared to the shallow architecture of the restricted Boltzmann machine. We benchmark the models, focussing on the accuracy of generating energetic observables near the phase transition, where these quantities are most difficult to approximate. Interestingly, after training the generative networks, we observe that the accuracy essentially depends only on the number of neurons in the first hidden layer of the network, and not on other model details such as network depth or model type. This is evidence that shallow networks are more efficient than deep networks at representing physical probability distributions associated with Ising systems near criticality.

cond-mat.dis-nn↗