We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the ``rigorous renormalization group.'' We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree--Fock-type treatment of the
z couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.
Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition, a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this Letter, we explore two entanglement properties that are promising for the study of the many-body localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We, thereby, give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al., Phys. Rev. B 88, 014206 (2013).
Eigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to dynamically probe nonequilibrium phases. In this work, we characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. Using tensor-network simulations, we observe oscillatory behavior of local expectation values and bipartite entanglement entropy. We explain these oscillations deep in the many-body localized spin-glass regime via a simple theoretical model. From perturbation theory, we predict the timescales up to which our analytical description is valid and confirm it with numerical simulations. Finally, we study the correlation length dynamics, which, after a long-time plateau, resume growing in line with renormalization group (RG) expectations. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems.
We investigate the ferromagnetic-glassy transitions that separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model with bond distribution $P(J)=p\ensuremath{\delta}(J\ensuremath{-}1)+(1\ensuremath{-}p)\ensuremath{\delta}(J+1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly reentrant. As a consequence, for an interval of the disorder parameter
p, around $p\ensuremath{\approx}0.77$, the system presents a low-temperature glassy phase, an intermediate ferromagnetic phase, and a high-temperature paramagnetic phase. Along the ferromagnetic-glassy transition line, magnetic correlations show a universal critical behavior with critical exponents $\ensuremath{\nu}=0.96(2)$ and $\ensuremath{\eta}=\ensuremath{-}0.39(2)$. The hyperscaling relation $\ensuremath{\beta}/\ensuremath{\nu}=(1+\ensuremath{\eta})/2$ is satisfied at the transitions, so that $\ensuremath{\beta}/\ensuremath{\nu}=0.305(10)$. This magnetic critical behavior represents a new universality class for ferromagnetic transitions in Ising-type disordered systems. Overlap correlations are apparently not critical and show a smooth behavior across the transition.
We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an
XY spin chain with
L spins, which experiences power-law decaying interactions in the form of ${V}_{ij}\ensuremath{\propto}1/{\left|i\ensuremath{-}j\right|}^{\ensuremath{\alpha}}$ (
i,j=1,...,L) and a random transverse field. By performing large-scale exact diagonalization for the chain size up to
L=18, we systematically analyze the energy gap statistics, the half-chain entanglement entropy, and the uncertainty of the entanglement entropy of the system at different interaction exponents $\ensuremath{\alpha}$. The finite-size critical scaling allows us to determine the critical disorder strength
Wc and the critical exponent $\ensuremath{\nu}$ at the many-body-localization phase transition, as a function of the interaction exponent $\ensuremath{\alpha}$ in the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$. We find that both
Wc and $\ensuremath{\nu}$ diverge when $\ensuremath{\alpha}$ decreases to a critical power of ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}1.16\ifmmode\pm\else\textpm\fi{}0.17$, indicating the absence of many-body localization for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$. Our result differs from the analytical prediction of ${\ensuremath{\alpha}}_{c}=3/2$ found in a previous work based on a scaling argument [A. L. Burin, Phys. Rev. B 92, 104428 (2015)], but is close to the recent numerical result ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$ obtained from quantum dynamics simulation [A. Safavi-Naini, M. L. Wall, O. L. Acevedo, A. M. Rey, and R. M. Nandkishore, Phys. Rev. A 99, 033610 (2019)].
Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\ensuremath{\alpha}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\ensuremath{\alpha}>\frac{1}{2}$. A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\ensuremath{\alpha}$, corresponding to a critical behavior with an effective central charge
c=ln(2), independent of $\ensuremath{\alpha}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\ensuremath{\alpha}$. For a wide range of partition size
l, the EE fits a critical behavior with a central charge close to
c=1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\ensuremath{\alpha}=2$. Only for small $l\ensuremath{\ll}L$, in a range which increases with the number of spins
N, we find deviations which are rather consistent with the strong disorder fixed point central charge
c=ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. We also present results obtained with DMRG and find agreement with ED for sufficiently small $\ensuremath{\alpha}<2$, whereas for larger $\ensuremath{\alpha}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.