arXiv subjects

Wen Wei Ho

Publications and source records attributed to Wen Wei Ho.

At least 55 records · Page 3Linked to original sources

arXiv2020

A Rigorous Theory of Prethermalization without Temperature

Prethermalization refers to the physical phenomenon where a system evolves toward some long-lived non-equilibrium steady state before eventual thermalization sets in. One general scenario where this occurs is in driven systems with dynamics governed by an effective Hamiltonian (in some rotating frame), such that ergodicity of the latter is responsible for the approach to the prethermal state. This begs the question whether it is possible to have a prethermal state not associated to any effective Hamiltonian. Here, we answer this question in the affirmative. We exhibit a natural class of systems in which the prethermal state is defined by emergent, global symmetries, but where the dynamics that takes the system to this state has no additional conservation laws, in particular energy. We explain how novel prethermal phases of matter can nevertheless emerge under such settings, distinct from those previously discussed.

quant-ph↗

arXiv2020

Quantum phases of Rydberg atoms on a kagome lattice

We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a novel regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.

cond-mat.quant-gas↗

arXiv2020

Spin transport in a tunable Heisenberg model realized with ultracold atoms

Simple models of interacting spins play an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, systems with gauge fields, high-Tc superconductors, and systems with exotic particles such as anyons and Majorana fermions. In order to study and compare these models, a versatile platform is needed. Realizing such a system has been a long-standing goal in the field of ultracold atoms. So far, spin transport has only been studied in the isotropic Heisenberg model. Here we implement the Heisenberg XXZ model with adjustable anisotropy and use this system to study spin transport far from equilibrium after quantum quenches from imprinted spin helix patterns. In the non-interacting XX model, we find ballistic behavior of spin dynamics, while in the isotropic XXX model, we find diffusive behavior. For positive anisotropies, the dynamics ranges from anomalous super-diffusion to sub-diffusion depending on anisotropy, whereas for negative anisotropies, we observe a crossover in the time domain from ballistic to diffusive transport. This behavior contrasts with expectations for the linear response regime and raises new questions in understanding quantum many-body dynamics far away from equilibrium.

cond-mat.quant-gas↗

arXiv2020

Quantum many-body scars from virtual entangled pairs

We study weak ergodicity breaking in a one-dimensional, nonintegrable spin-1 XY model. We construct for it an exact, highly excited eigenstate, which despite its large energy density, can be represented analytically by a finite bond-dimension matrix product state (MPS) with area-law entanglement. Upon a quench to a finite Zeeman field, the state undergoes periodic dynamics with perfect many-body revivals, in stark contrast to other generic initial states which instead rapidly thermalize. This dynamics can be completely understood in terms of the evolution of entangled virtual spin-1/2 degrees of freedom, which in turn underpin the presence of an extensive tower of strong-eigenstate thermalization hypothesis (ETH)-violating many-body eigenstates. The resulting quantum many-body scars are therefore of novel origin. Our results provide important analytical insights into the nature and entanglement structure of quantum many-body scars.

quant-ph↗

arXiv2020

Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.

cond-mat.str-el↗

arXiv2020

Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays

We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.

cond-mat.str-el↗

arXiv2019

Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions

State preparation protocols ideally require as minimal operations as possible, in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating non-trivial quantum states using the Variational Quantum-Classical Simulation (VQCS) protocol explored recently in [SciPost Phys. 6, 029 (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greene-Horne-Zeilinger (GHZ) states can be prepared with O(1) iterations of the protocol, and a quantum critical point of the long range transverse field Ising model (TFIM) can be prepared with > 99% fidelity on a 100 qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long range interactions.

cond-mat.str-el↗

arXiv2019

Efficient variational simulation of non-trivial quantum states

We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with $L$ variational parameters and physical runtimes $T$ that scale linearly with the system size $L$. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational ansätze as good descriptions of non-trivial states of matter.

cond-mat.str-el↗

arXiv2019

Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach

We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motions for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a theoretical framework for understanding quantum dynamics in a class of constrained spin models, which allow us to examine the recently suggested explanation of 'quantum many-body scarring' [Nature Physics (2018), doi:10.1038], and establish a connection to the corresponding phenomenon in chaotic single-particle systems.

quant-ph↗

arXiv2018

Emergent SU(2) dynamics and perfect quantum many-body scars

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasi-local deformation of the Rydberg blockade Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying non-integrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates - quantum many-body scars. Furthermore, using these insights, we construct a toy model that hosts exact quantum many-body scars, providing an intuitive explanation of their origin. Our results offer specific routes to enhancing coherent many-body revivals, and provide a step towards establishing the stability of quantum many-body scars in the thermodynamic limit.

quant-ph↗

arXiv2018

Floquet Mechanism for Non-Abelian Fractional Quantum Hall States

Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on bandstructure engineering via modulation of single-particle hopping terms. By systematically analyzing the resulting interactions using generalized pseudopotentials, we show that our Floquet-FQH approach leads to repulsive as well as attractive three-body interactions that are highly tunable and support a variety of non-Abelian multicomponent FQH states. Finally, we propose an implementation of the protocol in optically dressed ultracold polar molecules with modulated Rabi frequencies.

cond-mat.str-el↗

arXiv2018

Probing quantum thermalization of a disordered dipolar spin ensemble with discrete time-crystalline order

We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.

quant-ph↗

arXiv2018

Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^α$ with $α> d/2$. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.

cond-mat.dis-nn↗

arXiv2017

The Ergodicity Landscape of Quantum Theories

This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards, particles in random media, interacting spin or fermion systems). We find phenomenological relations between the onset of ergodicity (Gaussian-random delocalization of eigenstates) and the structure of the appropriate graphs, and we construct a heuristic picture of summing trajectories on graphs that describes why a generic interacting system should be ergodic. We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity. The result of this analysis is a rough but systematic outline of how ergodicity changes across the space of all theories with a given Hilbert space dimension. As a special case, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.

quant-ph↗

arXiv2017

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency $ν$. We prove that up to a quasi-exponential time $τ_* \sim e^{c \fracν{\log^3 ν}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $τ_*$, and hence this effective Hamiltonian is a conserved quantity up to $τ_*$. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction $U$ is much larger than the hopping $J$. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time $τ_*$ that is (almost) exponential in $U/J$.

math-ph↗

arXiv2017

Critical Time Crystals in Dipolar Systems

We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature 543, 221-225 (2017)]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.

cond-mat.dis-nn↗

arXiv2017

Universal edge information from wave-function deformation

It is well known that the bulk physics of a topological phase constrains its possible edge physics through the bulk-edge correspondence. Therefore, the different types of edge theories that a topological phase can host constitute a universal piece of data which can be used to characterize topological order. In this paper, we argue that, beginning from only the fixed-point wave function (FPW) of a nonchiral topological phase and by locally deforming it, all possible edge theories can be extracted from its entanglement Hamiltonian (EH). We give a general argument, and concretely illustrate our claim by deforming the FPW of the Wen-plaquette model, the quantum double of $\mathbb{Z}_2$. In that case, we show that the possible EHs of the deformed FPW reflect the known possible types of edge theories, which are generically gapped, but gapless if translational symmetry is preserved. We stress that our results do not require an underlying Hamiltonian--thus, this lends support to the notion that a topological phase is indeed characterized by only a set of quantum states and can be studied through its FPWs.

cond-mat.str-el↗

arXiv2017

Entanglement dynamics in quantum many-body systems

The dynamics of entanglement has recently been realized as a useful probe in studying ergodicity and its breakdown in quantum many-body systems. In this paper, we study theoretically the growth of entanglement in quantum many-body systems and propose a method to measure it experimentally. We show that entanglement growth is related to the spreading of local operators in real space. We present a simple toy model for ergodic systems in which linear spreading of operators results in a universal, linear in time growth of entanglement for initial product states, in contrast with the logarithmic growth of entanglement in many-body localized (MBL) systems. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of several copies of the original system, in which connections are controlled by a quantum switch (two-level system). By measuring only the switch's dynamics, the growth of the Rényi entropies can be extracted. Our work provides a way of understanding entanglement dynamics in many-body systems, and to directly measure its growth in time via a single local measurement.

cond-mat.stat-mech↗