arXiv subjects

Thomas Vojta

Publications and source records attributed to Thomas Vojta.

At least 145 records · Page 8Linked to original sources

arXiv2002

Infinite-randomness critical point in the itinerant quantum antiferromagnet

We study the quantum phase transition in the three-dimensional disordered itinerant antiferromagnet by Monte-Carlo simulations of the order-parameter field theory. We find strong evidence for the transition being controlled by an infinite-randomness fixed point: The dynamical scaling is activated, i.e., the logarithm of the energy scales like a power of the length, implying a dynamical exponent of infinity. The probability distribution of the energy gaps is very broad and becomes broader with increasing system size, even on a logarithmic scale.

cond-mat.dis-nn↗

arXiv2001

The Hartree-Fock based diagonalization - an efficient algorithm for the treatment of interacting electrons in disordered solids

The Hartree-Fock based diagonalization is a computational method for the investigation of the low-energy properties of correlated electrons in disordered solids. The method is related to the quantum-chemical configuration interaction approach. It consists in diagonalizing the Hamiltonian in a reduced Hilbert space built of the low-energy states of the corresponding disordered Hartree-Fock Hamiltonian. The properties of the method are discussed for the example of the quantum Coulomb glass, a lattice model of electrons in a random potential interacting via long-range Coulomb interaction. Particular attention is paid to the accuracy of the results as a function of the dimension of the reduced Hilbert space. It is argued that disorder actually helps the approximation.

cond-mat.dis-nn↗

arXiv2001

Localization and conductance in the quantum Coulomb glass

We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin. After introducing these models we explain our computational method, the Hartree-Fock based diagonalization. We then discuss the conductance and compare spinless fermions and electrons. It turns out that spin degrees of freedom do not play an essential role in the systems considered. Finally, we analyze localization and decay of single-particle excitations. We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.

cond-mat.dis-nn↗

arXiv2001

Superconductivity and Quantum Phase Transitions in Weak Itinerant Ferromagnets

It is argued that the phase transition in low-T_c clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical endpoint. A semi-quantitative discussion is given in terms of recent experiments on MnSi and UGe_2. It is then shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of magnons to the longitudinal magnetic susceptibility. This qualitatively explains the phase diagram recently observed in UGe_2 and ZrZn_2.

cond-mat.stat-mech↗

arXiv2001

Transport Anomalies and Marginal Fermi-Liquid Effects at a Quantum Critical Point

The conductivity and the tunneling density of states of disordered itinerant electrons in the vicinity of a ferromagnetic transition at low temperature are discussed. Critical fluctuations lead to nonanalytic frequency and temperature dependences that are distinct from the usual long-time tail effects in a disordered Fermi liquid. The crossover between these two types of behavior is proposed as an experimental check of recent theories of the quantum ferromagnetic critical behavior. In addition, the quasiparticle properties at criticality are shown to be those of a marginal Fermi liquid.

cond-mat.stat-mech↗

arXiv2001

Transport Anomalies and Marginal Fermi-Liquid Effects at a Quantum Critical Point

The behavior of the conductivity and the density of states, as well as the phase relaxation time, of disordered itinerant electrons across a quantum ferromagnetic transition is discussed. It is shown that critical fluctuations lead to anomalies in the temperature and energy dependence of the conductivity and the tunneling density of states, respectively, that are stronger than the usual weak-localization anomalies in a disordered Fermi liquid. This can be used as an experimental probe of the quantum critical behavior. The energy dependence of the phase relaxation time at criticality is shown to be that of a marginal Fermi liquid.

cond-mat.stat-mech↗

arXiv2001

Fock space localization, return probability, and conductance of disordered interacting electrons

We numerically simulate the low-energy properties of interacting electrons in a random potential using the Hartree-Fock based exact diagonalization method. In particular, we investigate how the transport properties are influenced by the combined effects of disorder and correlations in the presence of the electron spin. To this end we calculate the participation number of many-particle states in Fock space, the return probability of single-particle excitations, and the Kubo-Greenwood conductance. It turns out that in the strongly localized regime interactions increase the conductance whereas for weak disorder interactions decrease the conductance. In contrast, single-particle excitations in general experience a localizing influence of the interactions.

cond-mat.dis-nn↗

arXiv2000

Quantum phase transitions

Phase transitions which occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed are called quantum phase transitions. They are caused by quantum fluctuations which are a consequence of Heisenberg's uncertainty principle. These lecture notes give a pedagogical introduction to quantum phase transitions. After collecting a few basic facts about phase transitions and critical behavior we discuss the importance of quantum mechanics and the relation between quantum and classical transitions as well as their experimental relevance. As a primary example we then consider the Ising model in a transverse field. We also briefly discuss quantum phase transitions in itinerant electron systems and their connection to non-Fermi liquid behavior.

cond-mat.stat-mech↗

arXiv2000

The quantum phase transition of itinerant helimagnets

We investigate the quantum phase transition of itinerant electrons from a paramagnet to a state which displays long-period helical structures due to a Dzyaloshinskii instability of the ferromagnetic state. In particular, we study how the self-generated effective long-range interaction recently identified in itinerant quantum ferromagnets is cut-off by the helical ordering. We find that for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum phase transition is of second order with mean-field exponents. In contrast, for a weak Dzyaloshinskii instability the transition is analogous to that in itinerant quantum ferromagnets, i.e. it is of first order, as has been observed in MnSi.

cond-mat.stat-mech↗

arXiv2000

Disorder and Two-Particle Interaction in Low-Dimensional Quantum Systems

We review some of the recent results on two-interacting particles (TIP) in low-dimensional disordered quantum models. Special attention is given to the mapping of the problem onto random band matrices. In particular, we construct two simple, seemingly closely related examples for which an analogous mapping leads to incorrect results. We briefly discuss possible reasons for this discrepancy based on the physical differences between the TIP problem and our examples.

cond-mat.dis-nn↗

arXiv2000

Annealed disorder, rare regions, and local moments: A novel mechanism for metal-insulator transitions

Local magnetic moments in disordered sytems can be described in terms of annealed magnetic disorder, in addition to the underlying quenched disorder. It is shown that for noninteracting electron systems at zero temperature, the annealed disorder leads to a new mechanism, and a new universality class, for a metal-insulator transition. The transition is driven by a vanishing of the thermodynamic density susceptibility rather than by localization effects. The critical behavior near two-dimensions is determined, and the underlying physics is discussed.

cond-mat.stat-mech↗

arXiv2000

The effect of rare regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions $p<4$ the rare regions destroy the conventional critical behavior. For order parameter dimensions $p>4$ the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.

cond-mat.dis-nn↗

arXiv2000

From localization to delocalization in the quantum Coulomb glass

We numerically investigate how electron-electron interactions influence the transport properties of disordered electrons in two dimensions. Our study is based on the quantum Coulomb glass model appropriately generalized to include the spin degrees of freedom. In order to obtain the low-energy properties of this model we employ the Hartree-Fock based diagonalization, an efficient numerical method similar to the configuration interaction approach in quantum chemistry. We calculate the d.c. conductance by means of the Kubo-Greenwood formula and pay particular attention to the spin degrees of freedom. In agreement with earlier results we find that electron-electron interactions can cause delocalization. For spinful electrons this delocalization is significantly larger than for spinless electrons.

cond-mat.str-el↗

arXiv1999

Quantum critical behavior of itinerant ferromagnets

We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective long-range interaction between the spin fluctuations. This interaction turns out to be generically {\em antiferromagnetic} for clean systems. In disordered systems analogous correlation effects lead to even stronger singularities. The resulting long-range interaction is, however, generically ferromagnetic. We discuss two possibilities for the ferromagnetic quantum phase transition. In clean systems, the transition is generically of first order, as is experimentally observed in MnSi. However, under certain conditions the transition may be continuous with non-mean field critical behavior. In disordered systems, one finds a very rich phase diagram showing first order and continuous phase transitions and several multicritical points.

cond-mat.stat-mech↗

arXiv1999

Quantum phase transitions in electronic systems

Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quantum phase transitions occurring in electronic systems. The ferromagnetic transition of itinerant electrons shows a very rich behavior since the magnetization couples to additional electronic soft modes which generates an effective long-range interaction between the spin fluctuations. We then consider the influence of rare regions on quantum phase transitions in systems with quenched disorder, taking the antiferromagnetic transitions of itinerant electrons as a primary example. Finally we discuss some aspects of the metal-insulator transition in the presence of quenched disorder and interactions.

cond-mat.stat-mech↗

arXiv1999

Rare regions and annealed disorder in quantum phase transitions

The Griffiths region that is due to rare regions and the resulting local moments in disordered itinerant quantum magnets, and its influence on the critical behavior, is considered within the framework of an effective field theory. It is shown that the local moments can be described in terms of static, annealed disorder, and the physical consequences of this description are discussed.

cond-mat.stat-mech↗

arXiv1999

Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies Ω, small wavevectors k, and small m, the dispersion relation is found to be of the form Ω~ m^{1-α} k^2, with α= (4-d)/2 (2<d<4) for disordered systems, and α= (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), Ω~ m ln(1/m) k^2. Experiments to test these predictions are proposed.

cond-mat.str-el↗

arXiv1999

On the critical behavior of disordered quantum magnets: The relevance of rare regions

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.

cond-mat.stat-mech↗