We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

UR - https://arxiv.org/abs/1809.02614 ER - TY - JOUR T1 - Does a single eigenstate encode the full Hamiltonian? JF - Physical Review X Y1 - 2018 A1 - James R. Garrison A1 - Tarun Grover AB -The Eigenstate Thermalization Hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is ``thermal.'' Here we expound on this hypothesis by asking: for which class of operators, local or non-local, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities/temperatures using just a {single} eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a non-integrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and find that even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of \emph{all} operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle number conserving model at infinite temperature which substantiates our conjectures.

UR - https://journals.aps.org/prx/accepted/57078K7bAcf16207402997123fd00afaa074a0b75 ER - TY - JOUR T1 - Locality and digital quantum simulation of power-law interactions Y1 - 2018 A1 - Minh Cong Tran A1 - Andrew Y. Guo A1 - Yuan Su A1 - James R. Garrison A1 - Zachary Eldredge A1 - Michael Foss-Feig A1 - Andrew M. Childs A1 - Alexey V. Gorshkov AB -The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α>3D (where D is the number of dimensions).

UR - https://arxiv.org/abs/1808.05225 ER - TY - JOUR T1 - Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator Y1 - 2018 A1 - Su-Kuan Chu A1 - Guanyu Zhu A1 - James R. Garrison A1 - Zachary Eldredge A1 - Ana Valdés Curiel A1 - Przemyslaw Bienias A1 - I. B. Spielman A1 - Alexey V. Gorshkov AB -The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

UR - https://arxiv.org/abs/1807.11486 ER - TY - JOUR T1 - Unitary Entanglement Construction in Hierarchical Networks Y1 - 2018 A1 - Aniruddha Bapat A1 - Zachary Eldredge A1 - James R. Garrison A1 - Abhinav Desphande A1 - Frederic T. Chong A1 - Alexey V. Gorshkov AB -The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

UR - https://arxiv.org/abs/1808.07876 ER - TY - JOUR T1 - Extracting entanglement geometry from quantum states JF - Physical Review Letters Y1 - 2017 A1 - Katharine Hyatt A1 - James R. Garrison A1 - Bela Bauer AB -Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

VL - 119 UR - https://arxiv.org/abs/1704.01974 CP - 14 U5 - 10.1103/PhysRevLett.119.140502 ER - TY - JOUR T1 - Lieb-Robinson bounds on n-partite connected correlations JF - Physical Review A Y1 - 2017 A1 - Minh Cong Tran A1 - James R. Garrison A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an

We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a “volume law” to an “area law” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

VL - 95 U4 - 054204 UR - http://link.aps.org/doi/10.1103/PhysRevB.95.054204 U5 - 10.1103/PhysRevB.95.054204 ER -