Random Antiferromagnetic Chain

Ma, Shang‐keng; Dasgupta, Chandan; Hu, Chin‐Kun

doi:10.1103/physrevlett.43.1434

Cited by 445 publications

(567 citation statements)

References 5 publications

Supporting

Mentioning

545

Contrasting

Unclassified

Order By: Relevance

“…But in real systems, defects play a fundamental role. In fact, the random bond Heisenberg model has been extensively studied in the past beginning with the work of Ma and others (Bhatt and Lee, 1981;Dasgupta and Ma, 1980;Ma et al, 1979). Upon renormalization group flow, a given initial distribution of exchange couplings is converted to a power law distribution, leading to divergences with temperature in thermodynamic properties such as the bulk susceptibility.…”

Section: H Random Bond Modelsmentioning

confidence: 99%

Colloquium : Herbertsmithite and the search for the quantum spin liquid

2016

View full text Add to dashboard Cite

Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied, and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera's group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin 1 2 Heisenberg model on a kagome lattice. In this colloquium article, I will review these developments, and then discuss potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.

show abstract

Section: H Random Bond Modelsmentioning

confidence: 99%

Colloquium : Herbertsmithite and the search for the quantum spin liquid

2016

View full text Add to dashboard Cite

show abstract

“…As concerns the RSP, it was first obtained using a perturbative real-space renormalization group method introduced by Ma, Dasgupta and Hu (MDH) [19,20] to treat the spin-1/2 RE-HAC. This approach was proven to be asymptotically exact, which allowed for a fully characterization of the properties of the RSP [21].…”

Section: -Renormalization Group Approach For Random Quantum Spin Cmentioning

confidence: 99%

Entanglement entropy in random quantum spin-Schains

et al. 2007

View full text Add to dashboard Cite

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin-S. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude S of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2 chains using an asymptotically exact real-space renormalization group approach. I -INTRODUCTIONQuantum information science provides fruitful connections between different branches of physics. In this context, the relationship between entanglement, which is a fundamental resource for quantum information applications [1], and the theory of quantum critical phenomena [2,3] has been a focus of intensive research. Specifically, entanglement measures have been proposed as a tool to characterize quantum phase transitions (See, e.g., Refs. [4,5,6,7,8]). In this direction, a successful approach has been the analysis of bipartite entanglement in quantum systems as measured by the von Neumann entropy. Given a quantum system in a pure state |ψ and a bipartition of the system into two blocks A and B, entanglement between A and B can be measured by the von Neumann entropy S of the reduced density matrix of either block, i.e.,where ρ A = Tr B ρ and ρ B = Tr A ρ denote the reduced density matrices of blocks A and B, respectively, with ρ = |ψ ψ|. By evaluating S for quantum spin systems, Ref.[6] numerically found that entanglement displays a logarithmic scaling with the size of the block in critical (gapless) chains and saturates to a constant value in chains with a gap for excitations. The logarithmic scaling was proven in general for one-dimensional quantum models exhibiting conformal invariance [9,10], with the scaling governed by a universal factor, given by the central charge of the associated conformal field theory. Indeed, for a block of spins of length L in a quantum chain, von Neumann entropy S(L) scales aswhere c is the central charge and k is a non-universal constant. Recently, the behavior of entanglement entropy in critical spin chains has also been discussed in presence of disorder [11,12,13,14,15]. Disorder appears as an essential feature in a number of condensed matter systems, motivating a great deal of theoretical and experimental research (e.g., see [16,17]). Moreover, disorder usually introduces a further effect, namely, the breaking of conformal symmetry in a critical model. Remarkably, Refael and Moore [11] have shown that, even in the absence of conformal invariance, due to disorder, the logarithmic scaling given by Eq. (2) holds for the spin-1/2 rand...

show abstract

“…That this occurs for arbitrarily weak randomness, as it does, 8 cannot be convincingly shown by this RG as it is initially approximate when the distribution of J's is not broad. But its qualitative validity for weak randomness is suggested, since J e f f is always less than J l, r due to the prefactor 1 2 in Eq. ͑2͒.…”

mentioning

confidence: 99%

“…1. When a link forms between two spin 1 2 's ͓Fig. 2͑a͔͒, both spins disappear and the J e f f between the remaining neighboring spins is given by Eq.…”

mentioning

confidence: 99%

Spin reduction transition in spin-32random Heisenberg chains

2002

View full text Add to dashboard Cite

Random spin-3 2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S e f f ϭ 3 2 , while in the weak randomness phase the effective spins are S e f f ϭ 1 2 . Separating them is a quantum critical point near which there is a nontrivial mixture of spin-1 2 , spin-1, and spin-3 2 effective spins at low temperatures. Some of the most dramatic effects of randomness in solids appear in the low-temperature behavior of quantum systems. A ͑deceptively͒ simple class of such systems are random quantum spin chains, in particular, Heisenberg antiferromagnetic chains with the HamiltonianFrom a real-space renormalization-group ͑RG͒ analysis, 1 it has been shown that the spin-1 2 random antiferromagnetic ͑AFM͒ chain is strongly dominated by randomness at low temperatures even when the disorder is weak. 2 Its ground state is a random-singlet ͑RS͒ phase in which pairs of spins-mostly close together but occasionally arbitrarily far apart-form singlets. As the temperature is lowered, some of these singlets form at temperatures of order of the typical exchange and become inactive. But their neighboring spins will interact weakly across them via virtual triplet excitations. At lower temperatures, such further neighbors can form singlets and the process repeats. Concomitantly, the distribution of effective coupling strengths broadens rapidly. Eventually, singlets form on all length scales and the ground state is controlled by an RG fixed point with extremely strong disorder: an infinite randomness fixed point.This low-temperature behavior is in striking contrast to that of the pure spin-1 2 AFM chain, in which spin-spin correlations decay as x Ϫ1 because of long-wavelength lowenergy spin-wave ͑or spinon͒ modes. In the random-singlet phase, the average correlations decay as a power of distance -as x Ϫ2 -but for a very different reason: A typical pair of widely spaced spins will have only exponentially ͑in the square root of their separation͒ small correlations. But a small fraction, those that form a singlet pair, will have correlations of order unity independent of their separation; these rare pairs completely dominate the average correlations as well as the other low-temperature properties of the random system.Infinite randomness fixed points are ubiquitous in random quantum systems. They probably control phase discretesymmetry-breaking transitions in all random quantum systems -in any dimension 12 -and, in addition to the spin-1 2 AFM chain, also control the low-temperature properties of a range of random quantum phases. 15 Because of their ubiquity, further investigation of what types of random quantum phases and transitions can occur should shed light more generally on the combined roles of randomness and quantum fluctuations. The simplest cases to analyze are one dimensional because asymptotically exact RG's can be ...

show abstract

Random Antiferromagnetic Chain

Cited by 445 publications

References 5 publications

Colloquium : Herbertsmithite and the search for the quantum spin liquid

Colloquium : Herbertsmithite and the search for the quantum spin liquid

Entanglement entropy in random quantum spin-Schains

Spin reduction transition in spin-32random Heisenberg chains

Contact Info

Product

Resources

About