We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio $g=J/{J}^{\ensuremath{'}}$ in square-lattice dimerized $S=1/2$ Heisenberg antiferromagnets with intradimer and interdimer couplings $J$ and ${J}^{\ensuremath{'}}$. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy $\ensuremath{\nu}\ensuremath{\ge}1$. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where $\ensuremath{\nu}\ensuremath{\approx}0.71$). We discuss special circumstances which allow $\ensuremath{\nu}<1$ for the type of disorder considered here.We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio $g=J/{J}^{\ensuremath{'}}$ in square-lattice dimerized $S=1/2$ Heisenberg antiferromagnets with intradimer and interdimer couplings $J$ and ${J}^{\ensuremath{'}}$. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy $\ensuremath{\nu}\ensuremath{\ge}1$. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where $\ensuremath{\nu}\ensuremath{\approx}0.71$). We discuss special circumstances which allow $\ensuremath{\nu}<1$ for the type of disorder considered here.

arXiv:1006.1598Physical Review BNov 19, 201022 citations

Magnetic bound states in dimerized quantum spin systems

P. Lemmens, M. Fischer, M. Grove +5 more

arXiv:cond-mat/9809289Physica B Condensed MatterJan 1, 19996 citations

Criticality and Mott glass phase in a disordered two-dimensional quantum spin system

Nvsen Ma, Anders W. Sandvik, Dao‐Xin Yao

We use quantum Monte Carlo simulations to study a disordered $S=1/2$ Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which ${J}_{1}$ represents weak bonds, and ${J}_{2}$ and ${J}_{3}$ correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling $({J}_{2}+{J}_{3})/2$ , the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature $T=0$ ), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.We use quantum Monte Carlo simulations to study a disordered $S=1/2$ Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which ${J}_{1}$ represents weak bonds, and ${J}_{2}$ and ${J}_{3}$ correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling $({J}_{2}+{J}_{3})/2$, the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature $T=0$), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.

arXiv:1407.1113Physical Review BSep 26, 201413 citations

Critical phenomena in systems with long-range-correlated quenched disorder

Abel Weinrib, B. I. Halperin

As a model for a phase transition in an inhomogeneous system, we consider a system where the local transition temperature varies in space, with a correlation function obeying a power law $\ensuremath{\sim}{x}^{\ensuremath{-}a}$ for large separations $x$ . We extend the Harris criterion for this case, finding that for $a<d$ (where $d$ is the spatial dimension) the disorder is irrelevant if $a\ensuremath{\nu}\ensuremath{-}2>0$, while if $a>d$ we recover the usual Harris criterion: The disorder is irrelevant if $d\ensuremath{\nu}\ensuremath{-}2=\ensuremath{-}\ensuremath{\alpha}>0$. An $m$ -vector system of this type is studied with the use of a renormalization-group expansion in $\ensuremath{\epsilon}=4\ensuremath{-}d$ and $\ensuremath{\delta}=4\ensuremath{-}a$. We find a new long-range-disorder fixed point in addition to the short-range-disorder and pure fixed points found previously. The crossover between fixed points is found to follow the extended Harris criterion. The new fixed point has complex eigenvalues, leading to oscillating corrections to scaling, and has a correlation-length exponent $\ensuremath{\nu}=\frac{2}{a}$. We argue that this new scaling relation is exact and applies more generally than just to the specific model. We show that the extended Harris criterion also applies to percolation with long-range-correlated site or bond-occupation probabilities, so that the scaling law should be obeyed by such systems. Results for the percolation properties of the triangular Ising model are in agreement with these predictions.As a model for a phase transition in an inhomogeneous system, we consider a system where the local transition temperature varies in space, with a correlation function obeying a power law $\ensuremath{\sim}{x}^{\ensuremath{-}a}$ for large separations $x$. We extend the Harris criterion for this case, finding that for $a<d$ (where $d$ is the spatial dimension) the disorder is irrelevant if $a\ensuremath{\nu}\ensuremath{-}2>0$, while if $a>d$ we recover the usual Harris criterion: The disorder is irrelevant if $d\ensuremath{\nu}\ensuremath{-}2=\ensuremath{-}\ensuremath{\alpha}>0$. An $m$-vector system of this type is studied with the use of a renormalization-group expansion in $\ensuremath{\epsilon}=4\ensuremath{-}d$ and $\ensuremath{\delta}=4\ensuremath{-}a$. We find a new long-range-disorder fixed point in addition to the short-range-disorder and pure fixed points found previously. The crossover between fixed points is found to follow the extended Harris criterion. The new fixed point has complex eigenvalues, leading to oscillating corrections to scaling, and has a correlation-length exponent $\ensuremath{\nu}=\frac{2}{a}$. We argue that this new scaling relation is exact and applies more generally than just to the specific model. We show that the extended Harris criterion also applies to percolation with long-range-correlated site or bond-occupation probabilities, so that the scaling law should be obeyed by such systems. Results for the percolation properties of the triangular Ising model are in agreement with these predictions.

Physical review. B, Condensed matterJan 1, 1983437 citations

Constraints on Order and Disorder Parameters in Quantum Spin Chains

Michael Levin

arXiv:1903.09028Communications in Mathematical PhysicsJul 16, 202032 citations

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio $g=J/{J}^{\ensuremath{'}}$ in square-lattice dimerized

S=1/2

Heisenberg antiferromagnets with intradimer and interdimer couplings

J

and ${J}^{\ensuremath{'}}$. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy $\ensuremath{\nu}\ensuremath{\ge}1$. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where $\ensuremath{\nu}\ensuremath{\approx}0.71$). We discuss special circumstances which allow $\ensuremath{\nu}<1$ for the type of disorder considered here.

We use quantum Monte Carlo simulations to study a disordered

S=1/2

Heisenberg quantum spin model with three different nearest-neighbor interactions, ${J}_{1}\ensuremath{\le}{J}_{2}\ensuremath{\le}{J}_{3}$, on the square lattice. We consider the regime in which

{J}_{1}

represents weak bonds, and

{J}_{2}

and

{J}_{3}

correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled two-leg ladders. When increasing the average intradimer coupling

({J}_{2}+{J}_{3})/2

, the system undergoes a N\'eel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is of the gapless Mott glass type (i.e., in boson language it is incompressible at temperature

T=0

), and we find that the temperature dependence of the uniform magnetic susceptibility follows the stretched exponential form $\ensuremath{\chi}\ensuremath{\sim}exp(\ensuremath{-}b/{T}^{\ensuremath{\alpha}})$, with $0<\ensuremath{\alpha}<1$. At the N\'eel-glass transition, we observe the standard O(3) critical exponents, which implies that the Harris criterion for the relevance of the disorder is violated in this system.

x

. We extend the Harris criterion for this case, finding that for

a<d

(where

d

is the spatial dimension) the disorder is irrelevant if $a\ensuremath{\nu}\ensuremath{-}2>0$, while if

a>d

we recover the usual Harris criterion: The disorder is irrelevant if $d\ensuremath{\nu}\ensuremath{-}2=\ensuremath{-}\ensuremath{\alpha}>0$. An

m

-vector system of this type is studied with the use of a renormalization-group expansion in $\ensuremath{\epsilon}=4\ensuremath{-}d$ and $\ensuremath{\delta}=4\ensuremath{-}a$. We find a new long-range-disorder fixed point in addition to the short-range-disorder and pure fixed points found previously. The crossover between fixed points is found to follow the extended Harris criterion. The new fixed point has complex eigenvalues, leading to oscillating corrections to scaling, and has a correlation-length exponent $\ensuremath{\nu}=\frac{2}{a}$. We argue that this new scaling relation is exact and applies more generally than just to the specific model. We show that the extended Harris criterion also applies to percolation with long-range-correlated site or bond-occupation probabilities, so that the scaling law should be obeyed by such systems. Results for the percolation properties of the triangular Ising model are in agreement with these predictions.