Bulletin of the American Physical Society
2024 APS March Meeting
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session F31: Topology and Quantum Chaos in Many-Body Systems |
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Sponsoring Units: GSNP DQI DCMP Chair: Tan Van Vu, Riken Center for Quantum Computing Room: 102C |
Tuesday, March 5, 2024 8:00AM - 8:12AM |
F31.00001: Typical Entanglement Entropy in Systems with Particle Number Conservation Yale Cheng, Rohit Patil, Yicheng Zhang, Marcos Rigol, Lucas Hackl The bipartite entanglement entropy is a measure of quantum correlations and is conjectured to be a probe of quantum chaos when computed for random eigenstates of a physical Hamiltonian. We derive the entanglement entropy of random states with a fixed particle number in any system of indistinguishable particles including fermions, bosons, spin systems and mixtures thereof. Remarkably, we are able to determine all terms up to constant order, notably that the leading term scales with the volume of the subsystem and that the constant term is universal. We numerically compute the entanglement entropy of typical eigenstates of the spin-XXZ and Bose-Hubbard models and show it agrees with our result at leading order whenever model parameters are in the quantum chaotic regime, thereby providing further support of the aforementioned conjecture. |
Tuesday, March 5, 2024 8:12AM - 8:24AM |
F31.00002: Weak higher form symmetry breaking and decodabiilty transitions in mixed state topological orders Zhen Bi, Jianhao Zhang, Zhu-Xi Luo, Carolyn Zhang, Meng Cheng Understanding topologically ordered states in open quantum systems is both conceptually and practically important in the intersection of condensed matter and quantum information science. In this presentation, we consider topologically ordered mixed states through the lens of spontaneous symmetry breaking (SSB) tied to higher-form symmetry. In particular, we show how the decodability transition of topological order, when the state is under local decoherence, can be related to an SSB transition of a weak 1-form symmetry. By the standard Kramers-Wannier duality, this transition is also dual a transition between a traditional SSB and a strong-to-weak SSB phases of a 0-form symmetry. |
Tuesday, March 5, 2024 8:24AM - 8:36AM |
F31.00003: A study of dissipative models based on Dirac matrices Jyotsna Gidugu, Daniel P Arovas In this work, we generalize Shibata and Katsura's study (DOI: 10.1103/PhysRevB.99.174303) of a dissipative S=1/2 1d chain to two dimensions. Their model had a Hamiltonian with alternating XX and YY couplings on a 1d chain and Lindblad operators at each site describing the dissipation. They studied the dynamics of this system using the GKLS master equation and by identifying that it could be modeled as a non-hermitian Kitaev system on a two-leg ladder with a single Majorana species in the presence of a static Z2 gauge field. In our generalization to 2d, we consider a dissipative square lattice based on Gamma matrix spin operators which can be modeled as a non-Hermitian square lattice bilayer. It is again Kitaev-solvable. We identify the non-equilibrium steady states in the model. We identify the gauge invariant quantities and the constraints relating them and show how they can account for all the spin degrees of freedom. We show how a gauge can be chosen and proceed to look at the Liouvillian spectrum. We use a genetic algorithm to estimate the Liouvillian gap and the first decay modes for larger system sizes. We see a change in the dynamics as we change the dissipation strength and observe a transition in the first decay modes similar to that seen in Shibata and Katsura's work. To understand the behavior for small and large values of dissipation strength, we perform a perturbative analysis and compare the results obtained with our computational results. |
Tuesday, March 5, 2024 8:36AM - 8:48AM |
F31.00004: Mixed-state quantum anomaly and multipartite separability Leonardo Lessa, Meng Cheng, Chong Wang Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here we explore the surprising connection between symmetry-protected topology (SPT) and separability of their boundary mixed states. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G, where the anomaly is characterized by a bulk SPT invariant in the group cohomology Hd+2(G,U(1)). We show that any mixed state ρ that is strongly symmetric under G, in the sense that G ρ ∝ ρ, is necessarily (d+2)-nonseparable, i.e. is not the mixture of tensor products of d+2 states in the Hilbert space. Furthermore, such states cannot be prepared from any (d+2)-separable states using finite-depth local quantum channels, so the non-separability is long-ranged in nature. The anomaly-nonseparability connection also allows us to generate simple examples of mixed states with nontrivial multi-partite entanglement. |
Tuesday, March 5, 2024 8:48AM - 9:00AM |
F31.00005: The role of conformal symmetry and instability in determining the temperature of a causal diamond Pablo A Lopez-Duque, Carlos R Ordonez, Abhijit Chakraborty, Horacio E Camblong A finite-lifetime observer detects thermal particles in the Minkowski vacuum. Such an observer is constrained to a diamond shaped region in the flat spacetime -- known as a causal diamond. In the literature, it has been shown that the generator of the time evolution of a diamond observer is a non-compact SO(2,1) hyperbolic transformation generator $S$ and is intimately connected to conformal quantum mechanics (CQM). In this paper, using an explicit representation of this $S$ operator as described in the de Alfaro-Fubini-Furlan model involving the inverse square potential and the inverted harmonic oscillator potential, we explore the connection between CQM and thermality in causal diamonds via a semiclassical approach. In doing so, we probe the role of instability in determining the diamond temperature by using the Gutzwiller Trace Formula. We further make some comments about the quantum chaotic nature of the $S$ operator. |
Tuesday, March 5, 2024 9:00AM - 9:12AM |
F31.00006: Average Pure-State Entanglement Entropy in Spin Systems with SU(2) Symmetry Rohit Patil, Lucas Hackl, George R Fagan, Marcos Rigol We investigate the effect that the non-Abelian SU(2) symmetry has on the average entanglement entropy of highly excited Hamiltonian eigenstates and of random pure states. Focusing on sectors with a fixed total spin (and zero total magnetization), we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient is fixed by the appropriate dimension of the Hilbert space of the subsystem. While in the case of the highly excited eigenstates of integrable interacting Hamiltonians, we provide numerical evidence that the volume-law coefficient is smaller, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. We also discuss the nature of the subleading corrections. |
Tuesday, March 5, 2024 9:12AM - 9:24AM |
F31.00007: Minimally entangled microcanonical states Klee Pollock, Anatoly Dymarsky, Thomas Iadecola A recent conjecture inspired by black hole physics suggests that generic quantum many-body systems should admit finite-energy-density states with area-law entanglement and an energy variance that vanishes in the thermodynamic limit. This prediction is in sharp contradiction with intuition since finite-energy-density eigenstates of such systems exhibit volume-law entanglement. To test this hypothesis, we study a chaotic quantum spin chain using a numerical algorithm to minimize von-Neumann and Rényi entanglement entropies within narrow microcanonical energy windows. Our focus is on determining the emergent scaling relations governing how the minimal entanglement varies with window width. We comment on implications for the equivalence of quantum statistical ensembles and on the relation to quantum many-body scars. |
Tuesday, March 5, 2024 9:24AM - 9:36AM |
F31.00008: Entanglement patterns in many-body quantum systems constrained by spatial locality Joaquin Rodriguez-Nieva A long-standing question in the field of statistical mechanics has been describing the universal structure of quantum state ensembles characterizing physical many-body quantum systems. The widely-accepted expectation for "quantum chaotic" systems is that their eigenspectra and eigenstates display universal properties described by random matrix theory (RMT). However, eigenstates of physical systems also encode structure beyond RMT, notably spatial locality and symmetries. In this talk, I discuss how locality is imprinted in the structure of eigenstates in local Hamiltonian systems, leading to deviations from commonly-used RMT ensembles. I will show how, by appropriately constraining RMT ensembles, one can accurately describe the entanglement patterns of eigenstates in quantum chaotic systems. Second, I define a metric that compares the microcanonical entanglement distributions of eigenstates and appropriately-constrained RMT ensembles. Remarkably, we find rare regions in Hamiltonian parameter space where deviations from RMT are minimal, thus suggesting that "maximally chaotic" Hamiltonians---those exactly described by constrained RMT ensembles---may only exist in fine-tuned pockets of parameter space. |
Tuesday, March 5, 2024 9:36AM - 9:48AM |
F31.00009: Mixed-state Quantum Phases: Renormalization and Quantum Error Correction Shengqi Sang, Yijian Zou, Timothy Hsieh Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. |
Tuesday, March 5, 2024 9:48AM - 10:00AM |
F31.00010: Exploring Quantum Chaos through AFL Entropy: Insights from Perturbed Quantum Cat Maps Eric D Schultz, Laimei Nie, Keiichiro Furuya Dynamical entropies characterize chaos within a dynamical system. One such candidate for quantum dynamical systems is the Alicki-Fannes-Lindblad (AFL) entropy, which is closely related to the entropy exchange of quantum measurement. AFL entropy has been used to study certain quantum systems with a chaotic classical limit, where it recovers the classical Kolmogorov-Sinai entropy. However, some of these systems are not quantum chaotic, and the question arises as to whether quantum dynamical entropies can be used as a diagnosis for quantum chaos. To address this problem, we compute AFL entropy on the perturbed quantum cat maps, a class of single-particle quantum mechanical models that undergo transition between quantum chaotic and non-chaotic regimes when the perturbation strength is tuned. We compare the behaviors of AFL entropy in the early time between the two regimes. We also generalize our study to many-body systems such as the mixed-field Ising models. Furthermore, we discuss the relation and distinction between AFL entropy and other candidates of quantum dynamical entropies, in particular the Connes-Størmer entropy, and demonstrate it numerically in several models. |
Tuesday, March 5, 2024 10:00AM - 10:12AM |
F31.00011: Crystalline average symmetry-protected topological phases: Construction and classification Sarvesh Srinivasan, Jianhao Zhang, Zhen Bi Average symmetry-protected topological phases (ASPTs) are nontrivial phases of mixed quantum states that emerge in systems subjected to decoherence or disorder. These phases are protected by symmetries which may be violated in each individual realization of the system but are restored upon averaging over the ensemble. In recent work, it was shown that these phases may be constructed from domain-wall decoration and are mathematically characterized by a generalized spectral sequence [1,2]. In this work, we describe the construction of crystalline ASPTs in 2 and 3 dimensions, where the crystalline symmetries are averaged. Through a systematic method of block state construction, we establish the classification of average topological superconductors of all possible crystalline groups, for both trivial and nontrivial extensions of the crystalline symmetry by fermion parity. Remarkably, the generalized decorated domain wall construction allows us to identify examples of crystalline intrinsic ASPTs, which are phases that only emerge in the mixed state and cannot be realized in clean quantum systems. |
Tuesday, March 5, 2024 10:12AM - 10:24AM |
F31.00012: Dynamic Response of Dissipative Spin Chains Spenser Talkington, Martin Claassen One-dimensional spin chains are paradigmatic platforms to realize unusual phases and phase transitions in and out of equilibrium. Over the past ten years, boundary driven chains have emerged as a class of models exhibiting out-of-equilibrium quantum criticality. We develop a linear and non-linear response formalism for free fermionic and bosonic Lindbladian systems, which we use to study magnetic excitations, quantum criticality and dynamical responses in spin chains with boundary dissipation. In quantum Ising and XY spin chains, we find paramagnetic and spin-density wave (SDW) phases where the SDW wavelength diverges at a critical transverse field. In contrast to closed systems, the dynamic spin susceptibility hosts signatures of new non-equilibrium collective states evidenced by gapless modes. We then discuss dynamic response properties of finite-size spin chains with strong non-linearities such as the XXZ spin chain, and comment on possible implementations on NISQ quantum computing hardware |
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