We use a tensor network renormalization group method to study random
S=2 antiferromagnetic Heisenberg chains with alternating bond strength distributions. In the absence of randomness, an imposed dimerization with bond alternation induces two quantum critical points between the
S=2 Haldane phase, a partially dimerized phase, and a fully dimerized phase, depending on the strength of dimerization. These three phases, called ($\ensuremath{\sigma},4\ensuremath{-}\ensuremath{\sigma}$) = (2,2), (3,1), and (4,0) phases, are valence-bond solid (VBS) states characterized by $\ensuremath{\sigma}$ valence bonds (effective spin-1/2 singlet pairs) forming across even links and $4\ensuremath{-}\ensuremath{\sigma}$ valence bonds on odd links. Here we study the effects of bond randomness on the ground states of the dimerized spin chain, calculating disorder-averaged twist order parameters and spin correlations. We classify the types of random VBS phases depending on the strength of bond randomness
R and dimerization
D using the twist order parameter, which has a negative/positive sign for a VBS phase with odd/even $\ensuremath{\sigma}$. Our results demonstrate the existence of a multicritical point in the intermediate disorder regime with finite dimerization, where (2,2), (3,1), and (4,0) phases meet. This multicritical point is at the junction of three phase boundaries in the $R\text{\ensuremath{-}}D$ plane: the (2,2)-(3,1) and (3,1)-(4,0) boundaries that extend to zero randomness, and the (2,2)-(4,0) phase boundary that connects another multicritical point in the undimerized limit. The undimerized multicritical point separates a gapless Haldane phase and an infinite-randomness critical line with the diverging dynamic critical exponent in the large-
R limit at
D=0. Furthermore, we identify the (3,1)-(4,0) phase boundary as an infinite-randomness critical line even at small
R and find the signature of infinite randomness at the (2,2)-(3,1) phase boundary only in the vicinity of the multicritical point.
Using an adaptive strategy which enables the study of quenched disordered system via the density-matrix renormalization-group method, we compute the various ground-state spin-spin correlation measures of the spin-
21 antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean values of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in agreement with the predictions of the strong-disorder renormalization-group method. We do not find any hint of logarithmic corrections either in the bulk average correlations, which were recently reported by Shu et al. [Phys. Rev. B 94, 174442 (2016)], or in the end-to-end average correlations. We report the existence of a logarithmic correction on the end-to-end correlations of the clean chain. Finally, we have determined that the distribution of the bulk correlations, when properly rescaled by an associated Lyapunov exponent, is a narrow and universal (disorder-independent) probability function.
We study the low-energy physics of a broad class of time-reversal invariant and SU(2)-symmetric one-dimensional spin-
S systems in the presence of quenched disorder via a strong-disorder renormalization-group technique. We show that, in general, there is an antiferromagnetic phase with an emergent
SU(2S+1) symmetry. The ground state of this phase is a random singlet state in which the singlets are formed by pairs of spins. For integer spins, there is an additional antiferromagnetic phase which does not exhibit any emergent symmetry (except for
S=1). The corresponding ground state is a random singlet one but the singlets are formed mostly by trios of spins. In each case the corresponding low-energy dynamics is activated, i.e., with a formally infinite dynamical exponent, and related to distinct infinite-randomness fixed points. The phase diagram has two other phases with ferromagnetic tendencies: a disordered ferromagnetic phase and a large spin phase in which the effective disorder is asymptotically finite. In the latter case, the dynamical scaling is governed by a conventional power law with a finite dynamical exponent.
Using quantum Monte Carlo simulations, we study effects of disorder on the
S=1/2 Heisenberg model with exchange constant
J on the square lattice supplemented by multispin interactions
Q. It was found recently [L. Liu et al., Phys. Rev. X 8, 041040 (2018)] that the ground state of this $J\ensuremath{-}Q$ model with random couplings undergoes a quantum phase transition from the N\'eel antiferromagnetic state into a randomness-induced spin-liquid-like state that is a close analog to the well known random-singlet (RS) state of the Heisenberg chain with random couplings. This 2D RS state arises from a spontaneously symmetry-broken fourfold degenerate columnar valence-bond solid that is broken up by the disorder into finite domains, with spinons localized at topological defects. The interacting spinons form a critical collective many-body state without magnetic long range order but with the mean spin-spin correlations decaying with distance
r as ${r}^{\ensuremath{-}2}$, as in the one-dimensional RS state. The dynamic exponent $z\ensuremath{\ge}2$, varying continuously with the model parameters. In this work, we further investigate the properties of the RS state in the $J\ensuremath{-}Q$ model with random
Q couplings. We study the temperature dependence of the specific heat and various susceptibilities for large enough systems to reach the thermodynamic limit. We also analyze the size dependence of the critical magnetic order parameter and its susceptibility in the ground state. For all these quantities, we find consistency with the conventional quantum-critical scaling laws when the condition implied by the ${r}^{\ensuremath{-}2}$ form of the spin correlations is imposed. In particular, all the different quantities can be explained by the same value of the dynamic exponent
z at fixed model parameters. We argue that the RS state identified in the $J\ensuremath{-}Q$ model corresponds to a generic renormalization group fixed point that can be reached in many quantum magnets with random couplings and that it has already been observed experimentally.
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches is the tensor-network strong-disorder renormalization group (tSDRG), which was basically established for one-dimensional (1D) systems. In this paper, we propose a possible improvement of its algorithm toward 2D random spin systems, focusing on a generating process of the tree network structure of tensors, and precisely examine their performances for the random antiferromagnetic Heisenberg model not only on the 1D chain but also on the square- and triangular-lattices. On the basis of comparison with the exact numerical results up to 36 site systems, we demonstrate that accuracy of the optimal tSDRG algorithm is significantly improved for the 1D and 2D systems in the strong-randomness regime.
We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1\ensuremath{\le}{J}_{i}\ensuremath{\le}2)$ and uniformly distributed random transverse fields $({\mathrm{\ensuremath{\Gamma}}}_{0}\ensuremath{\le}{\mathrm{\ensuremath{\Gamma}}}_{i}\ensuremath{\le}2{\mathrm{\ensuremath{\Gamma}}}_{0})$ in the presence of a homogeneous longitudinal field,
h. Using different numerical techniques (density-matrix renormalization group, combinatorial optimization, and strong disorder renormalization group methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line $(h=0,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=1)$ there is an infinite disorder quantum fixed point, while at the other end $(h=2,\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Gamma}}}_{0}=0)$ there is a classical random first-order transition point. Close to this fixed point, for
h>2 and ${\mathrm{\ensuremath{\Gamma}}}_{0}>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.