Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T33: Nonergodic Dynamics Beyond Many-Body Localization |
Hide Abstracts |
Sponsoring Units: DCMP Chair: Michael Kolodrubetz, University of Texas at Dallas Room: Room 225 |
Thursday, March 9, 2023 11:30AM - 11:42AM |
T33.00001: A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars Biao Lian We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of $M$ sites with $N$ fermion modes per site, and has a conserved charge $Q$. It has an on-site chemical potential $mu$ with disorder $W$, and an interaction of strength $J$ restricting each fermion to excite two more fermions when moving forward by one site. We show the $N=3$ model with disorder $W=0$ show a Hilbert space fragmentation in all charge $Q$ sectors and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the $N=3$ model exhibits many-body localization (MBL) as $M ightarrowinfty$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests a MBL to quantum chaos crossover as $M/N$ decreases across $1$. At $W=0$, an exactly solvable many-body scar flat band exists in many charge $Q$ sectors, leading to measure nonzero number of quantum scar eigenstates in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows the model is in a breakdown (dielectric) phase when $mu/J1/2$). The breakdown is local when $M/Ngg1$, and is global when $M/Nll 1$. |
Thursday, March 9, 2023 11:42AM - 11:54AM |
T33.00002: Controlling dynamical many-body freezing via local driving Bhaskar Mukherjee, Ronald Melendrez, Hitesh J Changlani, Arijeet Pal Dynamics of periodically driven, interacting quantum systems can exhibit slow thermalization and freezing |
Thursday, March 9, 2023 11:54AM - 12:06PM |
T33.00003: Arrested Development and Fragmentation in Strongly-Interacting Floquet Systems Matthew Wampler, Israel Klich We explore how interactions can facilitate classical like dynamics in models with sequentially activated hopping. Specifically, we add local and short range interaction terms to the Hamiltonian, and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion. |
Thursday, March 9, 2023 12:06PM - 12:18PM |
T33.00004: Hilbert space fragmentation and interaction-induced localization in the extendedFermi-Hubbard model Philipp Frey, Lucas Hackl, Stephan Rachel We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest and next-nearest neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest and next-nearest neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest and next-nearest neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low. |
Thursday, March 9, 2023 12:18PM - 12:30PM |
T33.00005: Ergodicity breaking provably robust to arbitrary perturbations Oliver Hart, David T Stephen, Rahul Nandkishore We present a model that exhibits ergodicity breaking via Hilbert space fragmentation with an unprecedented level of robustness. The construction relies on a single prethermal conservation law and gives rise to an exponential number of frozen states when the conservation law is exact. These states persist to all finite orders in perturbation theory in the presence of arbitrary few-body perturbations; even those that are geometrically nonlocal or exhibit power-law tails. We additionally identify one-form $U(1)$ charges that label symmetry sectors without fragmentation, and argue that the asymptotic relaxation therein is described by magnetohydrodynamics of the emergent one-form symmetry. |
Thursday, March 9, 2023 12:30PM - 12:42PM |
T33.00006: Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries Alexey Khudorozhkov, Apoorv Tiwari, Claudio Chamon, Titus Neupert We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment. The model is not integrable, but violates the eigenstate thermalization hypothesis through an extensive Hilbert space fragmentation, including an exponential number of inert subsectors with trivial dynamics, arising from kinetic constraints. While subsystem symmetries are quite restrictive for the dynamics, we show that they alone cannot account for such a number of inert states, even with infinite-range interactions. We present a procedure for constructing shielding structures that can separate and disentangle dynamically active regions from each other. Notably, subsystem symmetries allow the thickness of the shields to be dependent only on the interaction range rather than on the size of the active regions, unlike in the case of generic dipole-conserving systems. |
Thursday, March 9, 2023 12:42PM - 12:54PM |
T33.00007: Fragmentation-induced localization and boundary charges in dimensions two and above Julius Lehmann, Pablo Sala de Torres-Solanot, Frank Pollmann, Tibor Rakovszky We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur's bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions. |
Thursday, March 9, 2023 12:54PM - 1:06PM |
T33.00008: Exact solution for the filling-induced thermalization transition in a 1D fracton system Brian J Skinner, Calvin Pozderac, David A Huse, Xiaozhou Feng, Steven Speck We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density nc. Specifically, when evolution proceeds by operators that act on s contiguous sites, the critical density is given by nc = 1/(s−2). We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent ν = 2. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: z = 4, while at the critical point it increases to zc > 6. |
Thursday, March 9, 2023 1:06PM - 1:18PM |
T33.00009: Prethermalization and the local robustness of gapped systems Chao Yin, Andrew Lucas We prove that prethermalization is a generic property of gapped local many-body quantum systems, subjected to small perturbations, in any spatial dimension. More precisely, let H0 be a Hamiltonian, spatially local in d spatial dimensions, with a gap Δ in the many-body spectrum; let V be a spatially local Hamiltonian consisting of a sum of local terms, each of which is bounded by ε << Δ. Then, the approximation that quantum dynamics is restricted to the low-energy subspace of H0 is accurate, in the correlation functions of local operators, for stretched exponential time scale τ ~ exp[(Δ/ε)^a] for any a<1/(2d-1). This result does not depend on whether the perturbation closes the gap. It significantly extends previous rigorous results on prethermalization in models where H0 was frustration-free. We infer the robustness of quantum simulation in low-energy subspaces, the existence of ``scarring" (strongly athermal correlation functions) in gapped systems subject to generic perturbations, the stability of false vacua in symmetry broken systems to non-perturbatively long times, and the robustness of quantum information in non-frustration-free gapped phases with topological order. |
Thursday, March 9, 2023 1:18PM - 1:30PM |
T33.00010: Unconventional Symmetries from Commutant Algebras Sanjay Moudgalya, Olexei I Motrunich The study of symmetry lies at the heart of various areas of physics. In equilibrium physics, symmetries are useful in classifying phases of matter, and in non-equilibrium physics, they are necessary to understand the phenomenon of thermalization. Most symmetries conventionally studied in the literature are examples of so-called on-site unitary symmetries. While such symmetries are sufficient to explain several physical phenomena, the recent discovery of weak violations of ergodicity in non-integrable quantum many-body systems, e.g., Hilbert space fragmentation and quantum many-body scarring, has called for a generalization of the notion of symmetry. The conventional theory of thermalization in quantum many-body systems demands that any simple initial state within a given symmetry sector explores the full Hilbert space of that sector under the dynamics of a symmetric Hamiltonian. However, in quantum many-body systems exhibiting weak ergodicity breaking, the Hilbert space possesses additional unexpected dynamically disconnected subspaces that cannot be explained in terms of on-site unitary symmetries, leading to a breakdown of conventional thermalization. In this talk, I will discuss a general mathematical framework to define symmetries based on so-called commutant algebras, which leads to a generalization of the notion of symmetry beyond on-site unitary ones. The unconventional symmetries revealed by this framework provide precise explanations for several dynamical phenomena ranging from weak ergodicity breaking to strong zero modes, allowing us to cast all of them into a single unified framework and also systematically construct local Hamiltonians that exhibit these phenomena. |
Thursday, March 9, 2023 1:30PM - 1:42PM Author not Attending |
T33.00011: Quantum scars and short-time survival probability in the PXP model Roya Radgohar, Martin Schnee, Stefanos Kourtis We characterize decay rate of survival probability, which is defined as the squared overlap amplitude between initial and time-evolved quantum state, in the PXP model with open boundary conditions. We investigate the role of anomalously slow thermalizing quantum states, so called quantum scar states, in determining the system's survival probability. We construct a theoretical model by splitting the local density of states (LDOS) into a Gaussian thermal contribution and a modulated Dirac comb describing the quantum scar contribution, and analytically calculate the survival probability. We find an exponential decay rate of the survival probability that increases linearly with the chain length, but with a nonuniversal slope that depends on the presence of scars in the LDOS. This agrees with our numerical results obtained by the time-evolving block-decimation (TEBD) method which allows us to compute the survival probability for PXP chains of up to 1000 qubits. Our results indicate that it is the contribution of quantum scars that dominates the survival probability decay in the short-time dynamics of the system. This is a signature of quantum scars that is readily measurable in existing experimental systems such as Rydberg atom quantum simulators. |
Thursday, March 9, 2023 1:42PM - 1:54PM |
T33.00012: Subharmonic Fidelity Revival of the Driven PXP model Haru K Park, SungBin Lee Recenrtly, PXP model has been studied as an example of the quantum scar, which contains a small portion of non-thermal eigenstates. This non-thermalness can be measured by the fidelity revival starting from certain pure state, which is also a key phenomenon in the quantum scar system. It has been reported that the temporal driving of the PXP model with certain amplitude enhances the fidelity revival. In this work, we show that the driven PXP model contains a subharmonic fidelity revival also. With free spin chain model, we have explained the origin of this subharmonic fidelity revival. |
Thursday, March 9, 2023 1:54PM - 2:06PM |
T33.00013: Quantum scars viewed as common eigenstates of simple bipartitions of scarred Hamiltonians and relations to quantum cellular automata. Pierre-Gabriel Rozon, Kartiek Agarwal, Michael J Gullans We discuss two new perspectives on quantum scars. |
Thursday, March 9, 2023 2:06PM - 2:18PM Author not Attending |
T33.00014: Peak structure of the infinite-temperature spectral function in scarred spin models Long Hin Tang The spectral function (transverse component of the dynamical structure factor) in spin models that exhibit long-lived scars exhibit peaks at the energy spacing of the scarred ladder at all temperatures. In quench experiments, this translates to underdamped oscillations in the corresponding local observable starting from typical initial states at the same frequency as that observed in quenches from the special scarred states. This is puzzling as the (exact) scars constitute a vanishing part of the many-body spectrum at large system sizes. In this talk, I will discuss how the peak structure arises from the proximity of the scarred models to models with an integer spectrum. Specifically, we attempt to quantitatively predict the quality factor of the oscillation and the widths of the peaks using Schrieffer-Wolff transformation near a paramagnet. |
Thursday, March 9, 2023 2:18PM - 2:30PM |
T33.00015: Antiscarring of Periodic Orbits Anton Graf, Joonas Keski-Rahkonen, Eric J Heller Although chaos plays an essential role in many natural phenomena, such as forecasting the weather, its quantum nature remains elusive. One of the most intriguing quantum chaotic phenomena is the scarring of a single-particle wavefunction showing an enhanced quantum probability density in the vicinity of a classically unstable periodic orbit. More recently, this conventional scaring has been accompanied by two new scarring phenomena, namely many-body and perturbation-induced scars. Here, we discuss a necessary consequence of quantum scarring, referred to as antiscarring: a depression of the probability density in other quantum states along the path of the scar-generating periodic orbit. Besides justifying the existence of antiscarring, we are elucidating the concept exemplarily for a disordered two-dimensional quantum well exhibiting strong perturbation-induced scars. Our results shed light upon understanding the fundamental dilemma posed by reconciling the quantum formalism with the classical concept of ergodicity, even in the presence of quantum-mechanical suppression of classical chaos, such as scars. In addition to providing an insight into the thermalization of a generic quantum system, this may pave a way towards employing scarring in future quantum devices. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700