Disorder-induced quantum-Griffiths-like features from a non-conventional renormalization group analysis near four dimensions

We investigate the role played by symmetry conserving quenched disorder on quantum criticality of a variety of d-dimensional systems with a continuous symmetry order parameter. We employ a non-standard procedure which combines a preliminary reduction to an effective classical random problem and a successive conventional renormalization group treatment. Solving the effective flow equations to first order in ε=4−d and then restoring the original coupling parameters, for d<4 we find a quantum critical point scenario exhibiting unusual features, which remind us of some predictions of the quantum Griffiths phase model.     

Quantum spherical model in a random field: coherent state path integral approach

By introducing boson operators, a quantum spherical XY model in the presence of a random field has been studied by the coherent state path integral approach. The phase diagram is obtained, and the effects of the random-field fluctuations on the possibilities of the existence of a ferromagnetic phase are discussed. At the critical point, , the order parameter M describing the ordered ferromagnetic phase disappears as .Since the model is equivalent to a Bose system, we also show that the phase transition at zero temperature between the superfluid and the disordered Mott insulator phases occurs at the chemical potential , where J₀ is the strength of the exchange interaction. As the temperature T goes to zero, the asymptotic behavior of the entropy and the specific heat are and , respectively. Received: 20 May 1997 / Accepted: 20 October 1997     

Crossing of specific heat curves in some correlated fermion systems

Specific heat versus temperature curves for various pressures, or magnetic fields (or some other external control parameter) have been seen to cross at a point or in a very small range of temperatures in many correlated fermion systems. We show that this behavior is related to the possibility of existence of a quantum critical point. Vicinity to a quantum critical point in these systems leads to a crossover from quantum to classical fluctuation regime at some temperature . The temperature at which the curves cross turns out to be near this crossover temperature. We have discussed the case of the normal phase of liquid Helium three and the heavy fermion systems CeAl₃ and UBe₁₃ in detail within the spin fluctuation theory, a theory which inherently contains a low energy scale which can be identified with . When the crossover scale is a homogeneous function of these control parameters there is always crossing at a point. We also mention other theories exhibiting a low energy scale near a quantum critical point and discuss this phenomenon in those theories. Received 25 June 1999     

Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of Cu2(C5H12N2)2Cl4>

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields H_c1 and H_c2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between H_c1 and H_c2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism. Received: 13 March 1998 / Received in final form and Accepted: 21 July 1998     

Anderson transition in 1D systems with spatial disorder

A simple Kronig-Penney model for 1D mesoscopic systems with δ peak potentials is used to study numerically the influence of spatial disorder on conductance fluctuations and distribution at different regimes. The Lévy laws are used to investigate the statistical properties of the eigenstates. It is found that an Anderson transition occurs even in 1D meaning that the disorder can also provide constructive quantum interferences. The critical disorder W_c for this transition is estimated. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results relative to conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models. At this transition, the conductance probability distribution has a system size independent shape with large fluctuations in good agreement with previous works.     

ZN Gauge theories on a lattice and quantum memory

In the present paper we shall study (2+1)-dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev’s model for quantum memory and quantum computations. Then we study effects of random gauge couplings (RGC) which are identified with noise and errors in quantum computations by Kitaev’s model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.     

Interaction versus dimerization in one-dimensional Fermi systems

In order to study the effect of interaction and lattice distortion on quantum coherence in one-dimensional Fermi systems, we calculate the ground state energy and the phase sensitivity of a ring of interacting spinless fermions on a dimerized lattice. Our numerical DMRG studies, in which we keep up to 1000 states for systems of about 100 sites, are supplemented by analytical considerations using bosonization techniques. We find a delocalized phase for an attractive interaction, which differs from that obtained for random lattice distortions. The extension of this delocalized phase depends strongly on the dimerization induced modification of the interaction. Taking into account the harmonic lattice energy, we find a dimerized ground state for a repulsive interaction only. The dimerization is suppressed at half filling, when the correlation gap becomes large. Received: 11 February 1998 / Revised: 1st April 1998 / Accepted: 30 April 1998     

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.     

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of , whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities. Received: 5 February 1998 / Accepted: 17 April 1998     

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T _c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T _c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T _c ⁽¹⁾ and T _c , which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T = 0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Effect of a fermion on quantum phase transitions in bosonic systems

The effect of a fermion with angular momentum j on quantum phase transitions of a (s,d) bosonic system is investigated. It is shown that the presence of a fermion strongly modifies the critical value at which the transition occurs, and its nature, even for small and moderate values of the coupling constant. The analogy with a bosonic system in an external field is mentioned. Experimental evidence for precursors of quantum phase transitions in bosonic systems plus a fermion (odd-even nuclei) is presented.     

Critical exponents of random XX and XY chains: Exact results via random walks

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent. Received 26 September 1999     

Quantum charge density fluctuations and the phase transition in Ce

We have calculated the quantum quadrupolar interaction due to charge density fluctuations of localized 4f-electrons in Ce by taking into account the angular dependence, the degeneracy of the localized 4f -orbitals and the spin-orbit coupling. The calculated crystal field of 4 f electronic states is in good agreement with neutron diffraction measurements. We show that orientational ordering of quantum quadrupoles drives a phase transition at K which we assign with the transformation. In the phase the centers of mass of the Ce atoms still form a face centered cubic lattice. The theory accounts for the first order character of the transition and for the cubic lattice contraction which accompanies the transition. The transition temperature increases linearly with pressure. Our approach does not involve Kondo spin fluctuations as the significant process for the phase transition. Received 19 October 1998     

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so‐called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitatively, and derive for the first time the (temperature—magnetic field) phase diagram, that contains Landau‐Fermi‐liquid, crossover and non‐Fermi liquid parts, thus resembling that of heavy‐fermion compounds.     

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ～ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erd?s-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.     

Interplay of metamagnetic and structural transitions in Ca2-xSrxRuO4

Metamagnetism in layered ruthenates has been interpreted as a novel kind of quantum critical behavior. In an external magnetic field, Ca_2-xSr_xRuO₄ undergoes a metamagnetic transition accompanied by a pronounced magnetostriction effect. In this paper we present a mean-field study for a microscopic model that naturally reproduces the key features of this system. The phase diagram calculated is equivalent to the experimental T-x phase diagram. The presented model also gives a good basis to discuss the critical metamagnetic behavior measured in the system.     

Spherical Model in a Random Field

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r ^4−d .