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Register a new userMaximally Random Discrete-Spin Systems with Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering
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Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states $q=3,4$ in $d$ dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d>1 and all non-infinite temperatures, the system eventually renormalizes to a random single state, thus signaling qxq degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1+epsilon, the system is as expected disordered at all temperatures for d=1.
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We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite temperature spin autocorrelation function decays at long times as $t^{-beta}$ with $beta < 0.5$, indicating subdiffusive transport at strong disorders.
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S=1/2 quantum spin chains and ladders with random exchange coupling are studied by using an effective low-energy field theory and transfer matrix methods. Effects of the nonlocal correlations of exchange couplings are investigated numerically. In particular we calculate localization length of magnons, density of states, correlation functions and multifractal exponents as a function of the correlation length of the exchange couplings. As the correlation length increases, there occurs a phase transition and the above quantities exhibit different behaviors in two phases. This suggests that the strong-randomness fixed point of the random spin chains and random-singlet state get unstable by the long-range correlations of the random exchange couplings.
In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or ``observable, states and (probably) unphysical, ``invisible states. We review replica symmetry breaking, and describe what it would mean in short-ranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot describe the low-temperature spin glass phase in any finite dimension. We then discuss the remaining possible scenarios that_could_ describe the low-temperature phase, and the differences they exhibit in some of their physical properties -- in particular, the interfaces that separate them. We also present rigorous results on metastable states and discuss their connection to thermodynamic states. Finally, we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^alpha$ with $alpha > d/2$. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.
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