日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians Analytical approaches are complemented by advanced numerical simulations

Anderson Transitions

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.

Superconducting phases of f -electron compounds

In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.

https://iopscience.iop.org/article/10.1088/0034-4885/66/12/R01/pdf

Quantum phase transitions

We investigate the entanglement entropy of a two-dimensional disordered system holographically. The disorder deforms a two-dimensional conformal field theory defined at a UV fixed point to a Lifshitz field theory in an IR region. After decomposing the entanglement entropy into short and long range correlations, we investigate how the entanglement entropy of the disordered system evolves from UV to IR along the renormalization group flow. The long range correlation interestingly leads to a universal critical exponent in the IR regime, which is only very weakly dependent on the strength of the disorder. We also investigate a possible phase transition and long range correlation between two subsystems by studying the mutual information.

Entanglement Entropy of Randomly Disordered System

We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-$s$-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the $p$-wave case, logarithmic corrections to scaling in all dimensions.

/pdf/order-parameter-symmetry-and-mode-coupling-effects-at-dirty-3fdxc91s5q.pdf

Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

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 $pl4,$ the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions $pg4,$ 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.

Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For superohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Influence of superohmic dissipation on a disordered quantum critical point

The $N$-color quantum Ashkin-Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin-Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers $N$, and the critical behavior for all $N \ne 4$. In the case of two colors, $N=2$, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all $N>2$, i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman-Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.

Rajesh Narayanan

Papers

Entanglement Entropy of Randomly Disordered System

Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

Effect of rare locally ordered regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

Influence of superohmic dissipation on a disordered quantum critical point

Strong-randomness phenomena in quantum Ashkin-Teller models