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Register a new userPerturbative instability of non-ergodic phases in non-Abelian quantum chains
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An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). This regime features a tree-like hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative non-ergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and time scales for thermalization: even if such chains eventually thermalize, they can exhibit non-ergodic dynamics up to parametrically long time scales with a non-analytic dependence on disorder strength.
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Strictly speaking the laws of the conventional Statistical Physics, based on the Equipartition Postulate and Ergodicity Hypothesis, apply only in the presence of a heat bath. Until recently this restriction was not important for real physical systems: a weak coupling with the bath was believed to be sufficient. However, the progress in both quantum gases and solid state coherent quantum devices demonstrates that the coupling to the bath can be reduced dramatically. To describe such systems properly one should revisit the very foundations of the Statistical Mechanics. We examine this general problem for the case of the Josephson junction chain and show that it displays a novel high temperature non-ergodic phase with finite resistance. With further increase of the temperature the system undergoes a transition to the fully localized state characterized by infinite resistance and exponentially long relaxation.
We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)$_k$ anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them quantum critical glasses. We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $krightarrowinfty$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel non-equilibrium critical phases of matter.
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.
The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two qubit density matrices allowed us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and allow us to exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.
We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, {the properties of the eigenstate-expectation distribution of the correlation and the scaling of the Inverse Participation Ratio averages.} We find that this ergodicity breaking {is different from many-body localization} because the average half-chain entanglement entropy of the eigenstates obeys volume law. This ergodicity breaking appears unrelated to the spectrum being organized in quasidegenerate multiplets at small hopping and finite system sizes, so in principle it can survive also for larger system sizes. We find that some imbalance oscillations in time which could mark the existence of a glassy behaviour in space are well described by the dynamics of a single symmetry-breaking doublet and {quantitatively} captured by a perturbative effective XXZ model. We show that the amplitude of these oscillations vanishes in the large-size limit. {Our findings are numerically obtained for systems with $L < 12$. Extrapolations of our scalings to larger system sizes should be taken with care, as discussed in the paper.
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