The two dimensional Antiferromagnetic Heisenberg model with next nearest neighbour Ising exchange

We have considered the $S=1/2$ antiferromagnetic Heisenberg model in two dimensions, with an additional Ising \nnn interaction. Antiferromagnetic \nnn interactions will lead to frustration, and the system responds with flipping the spins down in the $xy$ plane. For large next nearest neighbour coupling the system will order in a striped phase along the z axis, this phase is reached through a first order transition. We have considered two generalizations of this model, one with random \nnn interactions, and one with an enlarged unit cell, where only half of the atoms have \nnn interactions. In both cases the transition is softened to a second order transition separating two ordered states. In the latter case we have estimated the quantum critical exponent $\beta \approx 0.25$. These two cases then represent candidate examples of deconfined quantum criticality.Comment: Extensive revisions. Two new models with contious quantum phase transitio

Metallic spin glasses

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite temperature phase diagram is described and crossover functions are computed in mean field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.Comment: Contribution to the Proceedings of the ITP Santa Barbara conference on Non-Fermi liquids, 25 pages, requires IOP style file

Interface ordering and phase competition in a model Mott-insulator--band-insulator heterostructure

The phase diagram of model Mott-insulator--band-insulator heterostructures is studied using the semiclassical approximation to the dynamical-mean-field method as a function of thickness, coupling constant, and charge confinement. An interface-stabilized ferromagnetic phase is found, allow the study of its competition and possible coexistence with the antiferromagnetic order characteristic of the bulk Mott insulator.Comment: 5 pages, 3 figures, manuscript revised, results unchange

Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model

Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of $\rho_{s1} 2L$ and $\rho_{s2} 2L$, where $L$ stands for the spatial box size used in the simulations and $\rho_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in the $i$-direction. Remarkably, while we do observe a large correction to scaling for the observable $\rho_{s1}2L$ as proposed in \cite{Fritz11}, the data for $\rho_{s2}2L$ exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent $\nu$ which is consistent with the known O(3) result with moderate computational effort. Specifically, the numerical value of $\nu$ we determine by fitting the data points of $\rho_{s2}2L$ to their expected scaling form is given by $\nu=0.7120(16)$, which agrees quantitatively with the most accurate known Monte Carlo O(3) result $\nu = 0.7112(5)$. Finally, while we can also obtain a result of $\nu$ from the observable second Binder ratio $Q_2$ which is consistent with $\nu=0.7112(5)$, the uncertainty of $\nu$ calculated from $Q_2$ is more than twice as large as that of $\nu$ determined from $\rho_{s2}2L$.Comment: 7 figures, 1 table; brief repor

Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis

We compute specific heat of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice. We use a recently introduced technique to analyze high-temperature series expansion based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. In the case of kagome-lattice antiferromagnet, this method predicts a low-temperature peak at T/J<0.1.Comment: 6 pages, 5 color figures (.eps), Revtex 4. Change in version 3: Fig. 5 has been corrected (it now shows data for 3 different ground-state energies). The text is unchanged. v4: corrected an error in the temperature scale of Fig. 5. (text unchanged

Entanglement and Quantum Phase Transition Revisited

We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground state concurrence appears in the absence of quantum phase transition. It is opposed to the popular belief that the non-analyticity property of entanglement (ground state concurrence) can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground state concurrence in general can be more intricate than that of the ground state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the non-analyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, can not reveal quantum phase transition in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed.Comment: RevTeX 4, 4 pages, 1 EPS figures. some modifications in the text. Submitted to Phys. Rev.

Reduced dimensionality in layered quantum dimer magnets: Frustration vs. inhomogeneous condensates

Motivated by recent experiments on BaCuSi2O6, we investigate magnetic excitations and quantum phase transitions of layered dimer magnets with inter-layer frustration. We consider two scenarios, (A) a lattice with one dimer per unit cell and perfect inter-layer frustration, and (B) an enlarged unit cell with inequivalent layers, with and without perfect frustration. In all situations, the critical behavior at asymptotically low temperatures is three-dimensional, but the corresponding crossover scale may be tiny. Magnetic ordering in case (B) can be discussed in terms of two condensates; remarkably, perfect frustration renders the proximity effect ineffective. Then, the ordering transition will be generically split, with clear signatures in measurable properties. Using a generalized bond-operator method, we calculate the low-temperature magnetic properties in the paramagnetic and antiferromagnetic phases. Based on the available experimental data on BaCuSi2O6, we propose that scenario (B) with inequivalent layers and imperfect frustration is realized in this material, likely with an additional modulation of the inter-layer couling along the c axis.Comment: 23 pages, 18 figs, (v2) new fig for bandwidths, (v3) triplon binding energy discussed, (v4) small changes for clarification, accepted (PRB

Diamond chains with multiple-spin exchange interactions

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic four-fold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed, as well.Comment: 6 PRB pages, Added reference

Singular order parameter interaction at nematic quantum critical point in two dimensional electron systems

We analyze the infrared behavior of effective N-point interactions between order parameter fluctuations for nematic and other quantum critical electron systems with a scalar order parameter in two dimensions. The interactions exhibit a singular momentum and energy dependence and thus cannot be represented by local vertices. They diverge for all N greater or equal 4 in a collinear static limit, where energy variables scale to zero faster than momenta, and momenta become increasingly collinear. The degree of divergence is not reduced by any cancellations and renders all N-point interactions marginal. A truncation of the order parameter action at quartic or any other finite order is therefore not justified. The same conclusion can be drawn for the effective action describing fermions coupled to a U(1) gauge field in two dimensions.Comment: 18 pages, 1 figur

Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model

Lipkin model of arbitrary particle-number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunneling. Our new observation is that the well known quantum phase transition can also occur in the finite-N model only if N is an odd-number. We furthermore demonstrate a new type of quantum phase transition characterized by level-crossing which is induced by the geometric phase interference and is marvelously periodic with respect to the coupling parameter. Finally the conventional quantum phase transition is understood intuitively from the tunneling formulation in the thermodynamic limit.Comment: 4 figure