Assistant Professor, Physics, Stanford University (2019 - Present)
Junior Fellow, Harvard Society of Fellows (2016 - 2019)
Honors & Awards
William L. McMillan Award, University of Illinois Urbana-Champaign (2020)
George E. Valley Jr. Prize, American Physical Society (2020)
Early Career Award, U.S. Department of Energy (2020)
Sloan Fellowship, Alfred P. Sloan Foundation (2020)
Terman Fellowship, Stanford University (2019)
Joseph Taylor Fellowship, Department of Physics, Princeton University (2014)
Kusaka Prize, Department of Physics, Princeton University (2014)
Centennial Fellowship, Princeton University (2010-2014)
PhD, Princeton University, Physics (2016)
B.Sc., Harvey Mudd College, Physics (2010)
- Topics in Modern Condensed Matter Theory I: Many Body Quantum Dynamics
PHYSICS 470 (Spr)
- Independent Studies (2)
Prior Year Courses
- Asymmetric butterfly velocities in 2-local Hamiltonians SCIPOST PHYSICS 2020; 9 (2)
Probing entanglement in a many-body-localized system
2019; 364 (6437): 256-+
An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.
View details for DOI 10.1126/science.aau0818
View details for Web of Science ID 000464956600043
View details for PubMedID 31000657
- Signatures of integrability in the dynamics of Rydberg-blockaded chains PHYSICAL REVIEW B 2019; 99 (16)
- Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems PHYSICAL REVIEW B 2018; 98 (22)
- Mott, Floquet, and the response of periodically driven Anderson insulators PHYSICAL REVIEW B 2018; 98 (21)
- Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos PHYSICAL REVIEW B 2018; 98 (14)
- Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws PHYSICAL REVIEW X 2018; 8 (3)
Machine Learning Out-of-Equilibrium Phases of Matter
PHYSICAL REVIEW LETTERS
2018; 120 (25): 257204
Neural-network-based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized (MBL) or topological phases. Nevertheless, instances of machine learning offering new insights have been rare up to now. Here we show that a single feed-forward neural network can decode the defining structures of two distinct MBL phases and a thermalizing phase, using entanglement spectra obtained from individual eigenstates. For this, we introduce a simplicial geometry-based method for extracting multipartite phase boundaries. We find that this method outperforms conventional metrics for identifying MBL phase transitions, revealing a sharper phase boundary and shedding new insight on the topology of the phase diagram. Furthermore, the phase diagram we acquire from a single disorder configuration confirms that the machine-learning-based approach we establish here can enable speedy exploration of large phase spaces that can assist with the discovery of new MBL phases. To our knowledge, this Letter represents the first example of a standard machine learning approach revealing new information on phase transitions.
View details for DOI 10.1103/PhysRevLett.120.257204
View details for Web of Science ID 000435813300008
View details for PubMedID 29979078
Obtaining highly excited eigenstates of the localized XX chain via DMRG-X
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
2017; 375 (2108)
We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
View details for DOI 10.1098/rsta.2016.0431
View details for Web of Science ID 000413927000006
View details for PubMedID 29084883
View details for PubMedCentralID PMC5665784
- Defining time crystals via representation theory PHYSICAL REVIEW B 2017; 96 (11)
Two Universality Classes for the Many-Body Localization Transition
PHYSICAL REVIEW LETTERS
2017; 119 (7): 075702
We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.
View details for DOI 10.1103/PhysRevLett.119.075702
View details for Web of Science ID 000407719400008
View details for PubMedID 28949665
- Critical Properties of the Many-Body Localization Transition PHYSICAL REVIEW X 2017; 7 (2)
Observation of discrete time-crystalline order in a disordered dipolar many-body system
2017; 543 (7644): 221-+
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic 'time-crystalline' phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
View details for DOI 10.1038/nature21426
View details for Web of Science ID 000395688700034
View details for PubMedID 28277511
View details for PubMedCentralID PMC5349499
- A Floquet model for the many-body localization transition PHYSICAL REVIEW B 2016; 94 (22)
- Absolute stability and spatiotemporal long-range order in Floquet systems PHYSICAL REVIEW B 2016; 94 (8)
- Efficient variational diagonalization of fully many-body localized Hamiltonians PHYSICAL REVIEW B 2016; 94 (4)
QUANTUM SIMULATION Exploring the many-body localization transition in two dimensions
2016; 352 (6293): 1547–52
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.
View details for DOI 10.1126/science.aaf8834
View details for Web of Science ID 000378346500036
View details for PubMedID 27339981
Phase Structure of Driven Quantum Systems
PHYSICAL REVIEW LETTERS
2016; 116 (25): 250401
Clean and interacting periodically driven systems are believed to exhibit a single, trivial "infinite-temperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others-genuinely new to the Floquet problem-are characterized by order and nontrivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.
View details for DOI 10.1103/PhysRevLett.116.250401
View details for Web of Science ID 000378209900001
View details for PubMedID 27391704
Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach
PHYSICAL REVIEW LETTERS
2016; 116 (24): 247204
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
View details for DOI 10.1103/PhysRevLett.116.247204
View details for Web of Science ID 000378059500015
View details for PubMedID 27367405
- Low-frequency conductivity in many-body localized systems PHYSICAL REVIEW B 2015; 92 (10)
- Nonlocal adiabatic response of a localized system to local manipulations NATURE PHYSICS 2015; 11 (7): 560–65
- Eigenstate thermalization and representative states on subsystems PHYSICAL REVIEW E 2014; 90 (5)
How Universal Is the Entanglement Spectrum?
PHYSICAL REVIEW LETTERS
2014; 113 (6): 060501
It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this Letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low-energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the low-energy ES and the Rényi entropies can mislead entirely, while for quantum Hall systems, the ES has much less universal content than assumed to date.
View details for DOI 10.1103/PhysRevLett.113.060501
View details for Web of Science ID 000340034500001
View details for PubMedID 25148308
- Many-body localization and symmetry-protected topological order PHYSICAL REVIEW B 2014; 89 (14)
Eigenstate thermalization and representative states on subsystems.
Physical review. E, Statistical, nonlinear, and soft matter physics
2014; 90 (5-1): 052133
We consider a quantum system A∪B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of region A described without reference to its complement is traditionally assumed to require a reduced density matrix on A. While this is certainly true as an exact matter, we argue that under many interesting circumstances expectation values of typical operators anywhere inside A can be computed from a suitable pure state on A alone, with a controlled error. We use insights from quantum statistical mechanics-specifically the eigenstate thermalization hypothesis (ETH)-to argue for the existence of such "representative states."
View details for DOI 10.1103/PhysRevE.90.052133
View details for PubMedID 25493765
Kibble-Zurek scaling and string-net coarsening in topologically ordered systems
JOURNAL OF PHYSICS-CONDENSED MATTER
2013; 25 (40): 404214
We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now without the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the Abelian Z2 topologically ordered phase of the toric code/Z2 gauge theory, and the non-Abelian SU(2)k ordered phases of the relevant Levin-Wen models.
View details for DOI 10.1088/0953-8984/25/40/404214
View details for Web of Science ID 000324648200015
View details for PubMedID 24025618