02055nas a2200241 4500008004100000245005300041210005200094260001300146490000800159520125800167653002701425653004201452653003901494653003101533653004701564653005201611100002201663700002101685700002201706700002001728700002801748856003701776 2023 eng d00aNon-Abelian eigenstate thermalization hypothesis0 aNonAbelian eigenstate thermalization hypothesis c4/6/20230 v1303 a

The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aMurthy, Chaitanya1 aBabakhani, Arman1 aIniguez, Fernando1 aSrednicki, Mark1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2206.0531001840nas a2200253 4500008004100000245006100041210006000102260001400162520102500176653002701201653003901228653003101267653004701298653005201345100001401397700001301411700001701424700002301441700002501464700001801489700001801507700002401525856003701549 2022 eng d00aContinuous Symmetry Breaking in a Trapped-Ion Spin Chain0 aContinuous Symmetry Breaking in a TrappedIon Spin Chain c11/2/20223 a

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

10aFOS: Physical sciences10aQuantum Gases (cond-mat.quant-gas)10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aFeng, Lei1 aKatz, Or1 aHaack, Casey1 aMaghrebi, Mohammad1 aGorshkov, Alexey, V.1 aGong, Zhexuan1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2211.0127502003nas a2200217 4500008004100000245007300041210006900114260001300183520129800196653002701494653003101521653004701552100002001599700002201619700002101641700001601662700001801678700002401696700002801720856003701748 2022 eng d00aExperimental observation of thermalisation with noncommuting charges0 aExperimental observation of thermalisation with noncommuting cha c2/9/20223 a

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalisation. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-15 spins in an approximate microcanonical subspace, a generalisation of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)1 aKranzl, Florian1 aLasek, Aleksander1 aJoshi, Manoj, K.1 aKalev, Amir1 aBlatt, Rainer1 aRoos, Christian, F.1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2202.0465202034nas a2200217 4500008004100000245004900041210004900090260001300139520129000152653006101442653002701503653004201530653004701572653005201619100001901671700002001690700002901710700002101739700001901760856003701779 2022 eng d00aSpectral Form Factor of a Quantum Spin Glass0 aSpectral Form Factor of a Quantum Spin Glass c4/4/20223 a

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations -- the exponential of the spin glass "complexity" as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

10aDisordered Systems and Neural Networks (cond-mat.dis-nn)10aFOS: Physical sciences10aHigh Energy Physics - Theory (hep-th)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aWiner, Michael1 aBarney, Richard1 aBaldwin, Christopher, L.1 aGalitski, Victor1 aSwingle, Brian uhttps://arxiv.org/abs/2203.1275301780nas a2200181 4500008004100000245006700041210006600108260001500174520113500189653002701324653003101351653004701382653005201429100002201481700003201503700002601535856003701561 2021 eng d00aRelaxation of non-integrable systems and correlation functions0 aRelaxation of nonintegrable systems and correlation functions c12/17/20213 a

We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates coincide at a universal value that sets the timescales of processes at a finite energy density. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. We quantify this with the effective dimension of the state and with a state-observable effective dimension, which estimate the number of energy levels that participate in the dynamics. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians. This also allows to quantitatively understand the scope of previous theoretical results on equilibration timescales and on random matrix formalisms. We approach this problem with exact, full spectrum diagonalization. The numerics are carried out in a non-integrable Heisenberg-like Hamiltonian, and the dynamics are investigated for several pairs of observables and states.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aRiddell, Jonathon1 aGarcía-Pintos, Luis, Pedro1 aAlhambra, Álvaro, M. uhttps://arxiv.org/abs/2112.09475