Disorder effects in the quantum Heisenberg model: Extended dynamical mean-field theory analysis (original) (raw)
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Physical Review B, 2013
At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of "structural glasses" with a "random first-order transition" (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated, e.g., with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension, whereas despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.
Spin-glass transition in geometrically frustrated antiferromagnets with weak disorder
Physical Review B, 2010
We study the effect in geometrically frustrated antiferromagnets of weak, random variations in the strength of exchange interactions. Without disorder the simplest classical models for these systems have macroscopically degenerate ground states, and this degeneracy may prevent ordering at any temperature. Weak exchange randomness favours a small subset of these ground states and induces a spin-glass transition at an ordering temperature determined by the amplitude of modulations in interaction strength. We use the replica approach to formulate a theory for this transition, showing that it falls into the same universality class as conventional spin-glass transitions. In addition, we show that a model with a low concentration of defect bonds can be mapped onto a system of randomly located pseudospins that have dipolar effective interactions. We also present detailed results from Monte Carlo simulations of the classical Heisenberg antiferromagnet on the pyrochlore lattice with weak randomness in nearest neighbour exchange.
Thermodynamic properties of correlated fermions in lattices with spin-dependent disorder
New Journal of Physics, 2013
Motivated by the rapidly growing possibilities for experiments with ultracold atoms in optical lattices, we investigate the thermodynamic properties of correlated lattice fermions in the presence of an external spindependent random potential. The corresponding model, a Hubbard model with spin-dependent local random potentials, is solved within dynamical mean-field theory. This allows us to present a comprehensive picture of the thermodynamic properties of this system. In particular, we show that for a fixed total number of fermions spin-dependent disorder induces a magnetic polarization. The magnetic response of the polarized system differs from that of a system with conventional disorder.
Physical Review B, 2014
We explore the effect of the third-nearest neighbors on the magnetic properties of the Heisenberg model on an anisotropic triangular lattice. We obtain the phase diagram of the model using Schwinger boson mean-field theory. Competition between Néel, spiral, and collinear magnetically ordered phases is found as we vary the ratios of the nearest J 1 , next-nearest J 2 , and third-nearest J 3 neighbor exchange couplings. A spin-liquid phase is stabilized between the spiral and collinear ordered states when J 2 /J 1 1.8, for rather small J 3 /J 1 0.1. The lowest-energy two-spinon dispersions relevant to neutron scattering experiments are analyzed and compared to semiclassical magnon dispersions finding significant differences in the spiral and collinear phases between the two approaches. The results are discussed in the context of the anisotropic triangular materials: Cs 2 CuCl 4 and Cs 2 CuBr 4 and layered organic materials, κ-(BEDT-TTF) 2 X, and Y [Pd(dmit) 2 ] 2 .
Dephasing and Decorrelation of Spins in a Disordered Environment
2022
Dephasing of spins is a major roadblock to scaling up the size of quantum computing systems. We explore the possibility of utilizing highly disordered environments which are in the Many-Body Localized phase to arrest this dephasing. We embedded 2 'special' spins in such a highly disordered environment of Heisenberg spins to act as the target qubits and use the long-time value of the spin-spin correlator σi • σj as an order parameter to quantify the transition between the thermal and MBL phases of this system. It is seen that the dephasing between spins, as encoded in this correlator, is impeded in a disordered environment when the system is fully localized. The order parameter yields a critical exponent, to characterize the transition between the thermal and MBL phases, that appears to be robust to changes in microscopic parameters of the system or the choice of pair of spins.
Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction
2015
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect and aging phenomena. There are two main ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [ Phys. Rev. B 73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series 640, 012001 (2015)] reported SG ba...
Spin-Liquid State for Two-Dimensional Heisenberg Antiferromagnets on a Triangular Lattice
Modern Physics Letters B, 1998
The spin liquid state of the antiferromagnetic Heisenberg model on a triangular lattice is studied within the self-consistent Green's function method. It is shown that the spin excitation spectra is gapless, and ground-state energy per site is Eg/NJ=-0.966, which is in very good agreement with the results obtained within the variational Monte Carlo method based on the resonating-valence-bond state. Some thermodynamic properties are also discussed.
Coexistence of spin-glass and ferromagnetic order in the ±J Heisenberg spin-glass model
Physical Review B, 2007
simulations of the bond-frustrated ±J Heisenberg model confirm the existence of a finite temperature spin-glass transition at T SG = 0.220͑5͒. Remarkably, this transition temperature is composition dependent, rising to T SG = 0.25͑1͒ by the ferromagnet-spin-glass boundary. Coexistence of ferromagnetic and spin-glass ordering is observed at low frustration levels for T Ͻ T xy , and the composition dependence of this transition is also followed. The behavior we observe below T xy agrees with both the mean field prediction and the experimental observations while being inconsistent with "re-entrance," which demands a loss of ferromagnetic order. The complete phase diagram is presented.