Quantum Matter

We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal (h) fields. We show that, for all h, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional - argued to yield exact results at low frequencies - that expands in powers of a spin glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p-rotor model at nonzero h: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition.

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Zoom link https://pitp.zoom.us/j/98757418107?pwd=U1hiQnpKTDI4ajUyL04zRmQ4dVg3UT09

Driven by rapid advancements in quantum simulation capabilities across diverse physical platforms, open quantum systems are now of great interest, with special focus on thermalization processes of interacting many-body systems. Various techniques have been used to study operator spreading, to characterize entanglement dynamics, and even to identify exotic phases enabled by dynamical symmetries.

This talk will present a novel perspective on dynamical quantum systems that is capable of reproducing many previous results under a single intuitive framework and enables new results in symmetry-constrained systems. This is accomplished via a mapping between the dynamics averaged over Brownian random time evolution and the low-energy spectrum of a Lindblad superoperator, which acts as an effective Hamiltonian in a doubled Hilbert space. Doing so, we identify emergent hydrodynamics governing charge transport in open quantum systems with various symmetries, constraints, and ranges of interactions. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a simple, general, and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution, and by extension, thermalizing quantum systems.

O. Ogunnaike, J. Feldmeier, J.Y. Lee, "Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range Interactions," arXiv:2304.13028 (accepted to PRL)

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It is well-known that one-dimensional systems at finite temperature, such as the classical Ising model, cannot spontaneously break a discrete symmetry due to the proliferation of domain walls. The validity of this statement rests on a few assumptions, including the spatial locality of interactions. In a situation where a one-dimensional system exists as a defect in a critical, higher-dimensional bulk system, the coupling between defect and bulk can induce an effective long-range interaction on the defect. It is thus natural to ask if long-range order can be stabilized on a defect in a critical bulk, which amounts to asking whether domain walls on the defect are relevant or not in the renormalization group sense. I will explore this question in the context of Ising conformal field theory in two and higher dimensions in the presence of a localized symmetry-breaking field. With both perturbative techniques and numerical conformal bootstrap, I will provide evidence that indeed the defect domain wall must be relevant when 2 < d < 4. For the bootstrap calculations, it is essential to include “endpoint” primary fields of the defect, which lead to a rigorous and powerful way to input bulk data. I will additionally give tight estimates of a number of other quantities, including  scaling dimensions of defect operators and the defect entropy, and I will conclude with a discussion of future directions.

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Zoom link https://pitp.zoom.us/j/92671628591?pwd=WjNma3VEV2M4T011dFlLMzM2ZUJiUT09

In this talk, we identify anomalies of 1+1d lattice Hamiltonian systems as ’t Hooft anomalies. We consider anomalies in internal symmetries as well as Lieb-Schultz-Mattis (LSM) type anomalies involving lattice translations. Using topological defects, we derive a simple formula for the ‘anomaly cocycle’ and show it is the obstruction to gauging even on the lattice. We reach this by introducing a systematic procedure to gauge arbitrary internal symmetries on the lattice that may not act on-site. As a by-product of our gauging procedure, we construct non-invertible lattice translation symmetries from LSM anomalies.

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Zoom link https://pitp.zoom.us/j/98084408560?pwd=cllSVnpWcEhPK21aVDZubU4yYWNyQT09

Anomaly of global symmetry is an important tool to study dynamics of quantum systems. In recent years, new non-invertible global symmetries are discovered in many quantum systems such as the 2d Ising model, Standard Model like theories, and lattice models. I will discuss constraints on the dynamics in 3+1d systems using anomalies of non-invertible symmetries from the perspective of bulk-boundary correspondence. The discussion is based on the work https://arxiv.org/abs/2308.11706 with Clay Cordova and Carolyn Zhang.

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Zoom link https://pitp.zoom.us/j/99162815973?pwd=M01nZXJIN2tCRjhuZlljNU1id01XQT09

I will introduce a new picture of quantum dynamics that might be thought of as "gauging" Schrodinger's picture that results in many "local" Hilbert spaces [1]. Truncating the dimensions of the local Hilbert spaces in this new picture yields an exciting new kind of tensor network whose computational cost does not increase with increasing spatial dimension (for fixed bond dimension) [2]. More detail: Although quantum dynamics are local for local Hamiltonians, the locality is not explicit in the Schrodinger picture since the wavefunction amplitudes do not obey a local equation of motion. In the first part of this talk, I will introduce a new picture of quantum dynamics—the gauge picture—which is similar to Schrodinger's picture, but with the feature that spatial locality is explicit in the equations of motion. In a sense, the gauge picture might be thought of as the result of "gauging" the global unitary symmetry of quantum dynamics into a local symmetry[1]. In the second part of the talk, I discuss a new kind of tensor network ansatz that is inspired from the gauge picture. In the gauge picture, different regions of space are associated with different Hilbert spaces, which are related by gauge connections. By relaxing the unitary constraint on the gauge connections, we can truncate the Hilbert space dimensions associated with different regions to obtain an approximate description of quantum dynamics. This truncated gauge picture, which we dub "quantum gauge network", is intriguingly similar to a classical lattice gauge theory coupled to a Higgs field (which are "local" wavefunctions in the gauge picture), but with non-unitary connections. In one spatial dimension, a quantum gauge network can be easily mapped to a matrix product density operator, and a matrix product state can be mapped to a quantum gauge network. Unlike tensor networks such as PEPS, quantum gauge networks boast the advantage that for fixed bond dimension, the computational cost does not increase with the number of spatial dimensions! Encoding fermionic wavefunctions is also remarkably straightforward. We provide a simple algorithm for approximately simulating quantum dynamics of bosonic or fermionic Hamiltonians in any spatial dimension. We compare the new quantum dynamics algorithm to exact methods for fermion systems in up to three spatial dimensions [2]. [1] The Gauge Picture of Quantum Dynamics. arXiv:2210.09314 [2] Quantum Gauge Networks: A New Kind of Tensor Network. arXiv:2210.12151

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Zoom link: https://pitp.zoom.us/j/94596192271?pwd=MytzNUx4ZEZEemkvcEEzbllWM1J6QT09

Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.

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Zoom link: https://pitp.zoom.us/j/95381972217?pwd=Ni9iQ2hrUVNnWTJERDRmZk9GaW1jZz09

The presence of many competing classical ground states in frustrated magnets implies that quantum fluctuations may stabilize quantum spin liquids (QSL), which are characterized by fractionalized excitations and emergent gauge fields. A paradigmatic example is the U(1) Dirac spin liquid (DSL), which at low-energies is described by emergent quantum electrodynamics in 2+1 dimensions (QED3), a strongly interacting field theory with conformal symmetry. While the DSL is believed to be intrinsically stable, its robustness against various other couplings has been largely unexplored and is a timely question, also given recent experiments on triangular-lattice rare-earth oxides. In this talk, using complementary perturbation theory and scaling arguments as well as results from numerical DMRG simulations, I will show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) valence-bond solid state. Away from the limit of static distortions, I will argue that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable.

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Zoom link https://pitp.zoom.us/j/96764903405?pwd=Y0gyU3hGSC9va0hzWnZRZFBOVmRCZz09

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

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Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

Zoom Link: TBD