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It is well-known that spontaneous symmetry breaking in one spatial dimension is thermodynamically forbidden at finite energy density. Here we show that mirror-symmetric disorder in an interacting quantum system can invert this paradigm, yielding spontaneous breaking of mirror symmetry only at finite energy density and giving rise to mirror-glass order. The mirror-glass transition, which is driven by a finite density of interacting excitations, is enabled by many-body localization, and appears to occur simultaneously with the localization transition. This counterintuitive manifestation of localization-protected order can be viewed as a quantum analog of inverse freezing, a phenomenon that occurs, e.g., in certain models of classical spin glasses.
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Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here we study quantum dynamics of an isolated 1d spin-glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via resonance avalanche mechanism, that is also responsible for the destruction of MBL in non-glassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.
In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The Grand Canonical Potential is obtained within the static approximation and one-step replica symmetry breaking scheme. As a result, phase diagrams temperature {it versus} the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.
The ferromagnetic phase of an Ising model in d=3, with any amount of quenched antiferromagnetic bond randomness, is shown to undergo a transition to a spin-glass phase under sufficient quenched bond dilution. This general result, demonstrated here with the numerically exact renormalization-group solution of a d=3 hierarchical lattice, is expected to hold true generally, for the cubic lattice and for quenched site dilution. Conversely, in the ferromagnetic-spinglass-antiferromagnetic phase diagram, the spin-glass phase expands under quenched dilution at the expense of the ferromagnetic and antiferromagnetic phases. In the ferro-spinglass phase transition induced by quenched dilution reentrance is seen, as previously found for the ferro-spinglass transition induced by increasing the antiferromagnetic bond concentration.
We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y2Mo2O7, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical randomness to each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielectric non-linear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization group transformation. These discrete sequences are therefore fixed points of a emph{functional} renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.
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