Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions (original) (raw)
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Quantum critical behavior of a three-dimensional superfluid-Mott glass transition
Physical Review B, 2018
The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent ν = 1/2 violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc = 0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z = 1.67(6), ν = 0.90(5), β/ν = 1.09(3), and γ/ν = 2.50(3). The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.
Deconfined quantum criticality and logarithmic violations of scaling from emergent gauge symmetry
Physical Review B, 2012
We show that the low-energy effective theory for a deconfined quantum critical point in d = 2 + 1 dimensions as described by the Sachdev-Jalabert lattice model contains at leading order a contribution given by the Faddeev-Skyrme model. We use the CP N−1 representation to derive the leading contribution to the spin stiffness at large N near the quantum critical point and show that it exhibits a logarithmic correction to scaling of the same type as the one recently observed numerically in the so called J − Q model. Much of our understanding of phase transitions is based on the concept of spontaneous symmetry breaking [1], which provides a mechanism for the spontaneous generation of an ordered state as one or more parameters of a many-body system are varied. In Abelian systems the ordered state can be related to the disordered, symmetric one by a duality transformation which maps a strongly coupled regime into a waekly coupled one . In the case of an U(1) symmetry the unbroken symmetry phase is described in the dual picture by a disordered parameter , as opposed to the order parameter describing the broken symmetry state in the original picture. The disorder parameter is in this case nonzero when the vortices are condensed, meaning that the U(1) symmetry of the dual theory is spontaneously broken. In this picture the superfluid phase corresponds to the regime where the symmetry is unbroken. The vortex condensation of the dual theory reflects the nontriviality of the first homotopy group associated to the U(1) symmetry, i.e., π 1 (U(1)) = Z, the group of integers. This leads, for instance, to the flux quantization phenomenon in superconductors.
Physical Review B, 2012
In this paper we investigate the quantum phase transition from magnetic Bose glass to magnetic Bose-Einstein condensation induced by a magnetic field in NiCl2·4SC(NH2)2 (dichloro-tetrakis-thiourea-Nickel, or DTN), doped with Br (Br-DTN) or site diluted. Quantum Monte Carlo simulations for the quantum phase transition of the model Hamiltonian for Br-DTN, as well as for site-diluted DTN, are consistent with conventional scaling at the quantum critical point and with a critical exponent z verifying the prediction z = d; moreover the correlation length exponent is found to be ν = 0.75(10), and the order parameter exponent to be β = 0.95(10). We investigate the low-temperature thermodynamics at the quantum critical field of Br-DTN both numerically and experimentally, and extract the power-law behavior of the magnetization and of the specific heat. Our results for the exponents of the power laws, as well as previous results for the scaling of the critical temperature to magnetic ordering with the applied field, are incompatible with the conventional crossover-scaling Ansatz proposed by Fisher et al., [Phys. Rev. B 40, 546 (1989)], but they can all be reconciled within a phenomenological Ansatz in the presence of a dangerously irrelevant operator.
Particle-Hole Symmetry and the Bose Glass to Superfluid Transition
Physical Review Letters, 1996
The generic Hamiltonian describing the zero temperature transition between the insulating Bose glass phase and the superfluid phase lacks particle-hole symmetry, but a statistical version of this symmetry is believed to be restored at the critical point. We show that the renormalization group relevance of particle-hole asymmetry may be explored in a controlled fashion only for small time dimensions, e t ø 1, where we find a stable particle-hole asymmetric and an unstable particle-hole symmetric fixed point, but we provide evidence that the two merge for some finite e t ഠ 2 3 , which tends to confirm symmetry restoration at the physical e t 1. PACS numbers: 74.20.Mn, 05.30.Jp, 05.70.Jk, 64.70.Pf The zero temperature superfluid-insulator transition of bosons in a random external potential [1] is an interesting and incompletely understood example of a quantum phase transition. Experimental realizations include 4 He in porous media [2], granular and amorphous superconductors , and perhaps the pinning of flux lines by columnar defects in high temperature superconductors .
Quantum criticality: beyond the Landau-Ginzburg-Wilson paradigm
Physical Review B, 2004
We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Néel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a secondorder quantum phase transition. This conflicts with Landau-Ginzburg-Wilson theory, which predicts that such states with distinct broken symmetries are generically separated either by a first-order transition, or by a phase with co-existing orders. The critical theory of the second-order transition is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.
Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability
Physical Review B, 2012
We use the renormalization group method to study normal state properties of quasi-onedimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas, the integration of the renormalization group equations for the two-loop single particle Matsubara self-energy leads to a nonFermi-liquid temperature downturn of the momentum-resolved quasi-particle weight over most part of the Fermi surface. The amplitude of the downturn correlates with the entire instability line for superconductivity, defining an extended quantum critical region of the phase diagram as a function of nesting deviations of the Fermi surface. One also extracts the downward renormalization of interchain hopping amplitudes at arbitrary low temperature in the normal phase. By means of analytical continuation of the Matsubara self-energy, one-particle spectral functions are obtained with respect to both energy and temperature and their anomalous features analyzed in connection with the sequence of instability lines of the phase diagram. The quasi-particle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic T dependences. The nonFermi-liquid linear-T component correlates with the temperature scale Tc of the superconducting instability over an extended range of nesting deviations, whereas its anisotropy along the Fermi surface is predicted to parallel the momentum profile of a d-wave pairing gap on the Fermi surface. We examine the implications of our results for low dimensional unconventional superconductors, in particular the Bechgaard salts series of quasi-one-dimensional organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.
Quantum critical behavior of a three-dimensional Ising spin glass in a transverse magnetic field
Physical Review Letters, 1994
The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent ν = 1/2 violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc = 0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z = 1.67(6), ν = 0.90(5), β/ν = 1.09(3), and γ/ν = 2.50(3). The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.
Role of disorder on the quantum critical point of a model for heavy fermions
Physical Review B, 2001
A zero temperature real space renormalization group (RG) approach is used to investigate the role of disorder near the quantum critical point (QCP) of a Kondo necklace (XY-KN) model. In the pure case this approach yields Jc = 0 implying that any coupling J = 0 between the local moments and the conduction electrons leads to a non-magnetic phase. We also consider an anisotropic version of the model (X − KN), for which there is a quantum phase transition at a finite value of the ratio between the coupling and the bandwidth, (J/W). Disorder is introduced either in the onsite interactions or in the hopping terms. We find that in both cases randomness is irrelevant in the X − KN model, i.e., the disorder induced magnetic-non-magnetic quantum phase transition is controlled by the same exponents of the pure case. Finally, we show the fixed point distributions PJ (J/W) at the atractors of the disordered, non-magnetic phases.
Physical Review B, 2020
We study the behavior of the entropy of the pseudogap Bose-Fermi Kondo model within a dynamical large-N limit, where N is related to the symmetry group of the model. This model is a general quantum impurity model that describes a localized level coupled to a fermionic bath having a density of states that vanishes in a powerlaw fashion near the Fermi energy and to a bosonic bath possessing a powerlaw spectral density below a cutoff energy. As a function of the couplings to the baths various quantum phase transitions can occur. We study how the impurity entropy changes across these zero-temperature transitions and compare our results with predictions based on the gtheorem. This is accomplished by an analysis of the leading and sub-leading scaling behavior. Our analysis shows that the g-theorem does not apply to the pseudogap Bose-Fermi Kondo model at the large-N level. This inapplicability originates from an anomalous contribution to the scaling function in the hydrodynamic regime where kBT > ω which is absent in the quantum coherent regime, i.e., for kBT < ω. We also compare our results with those obtained for the Sachdev-Ye-Kitaev or SYK model.
Quantum Critical Scaling of Dirty Bosons in Two Dimensions
We determine the dynamical critical exponent, z, appearing at the Bose glass to superfluid transition in two dimensions by performing large scale numerical studies of two microscopically different quantum models within the universality class; The hard-core boson model and the quantum rotor (soft core) model, both subject to strong on-site disorder. By performing many simulations at different system size, L, and inverse temperature, β, close to the quantum critical point, the position of the critical point and the critical exponents, z, ν and η can be determined independently of any prior assumptions of the numerical value of z. This is done by a careful scaling analysis close to the critical point with a particular focus on the temperature dependence of the scaling functions. For the hard-core boson model we find z = 1.88(8), ν = 0.99(3) and η = −0.16(8) with a critical field of hc = 4.79(3), while for the quantum rotor model we find z = 1.99(5), ν = 1.00(2) and η = −0.3(1) with a critical hopping parameter of tc = 0.0760(5). In both cases do we find a correlation length exponent consistent with ν = 1, saturating the bound ν ≥ 2/d as well as a value of z significantly larger than previous studies, and for the quantum rotor model consistent with z = d.