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Journal of the Physical Society of Japan

Mott Transition and Transition to Incompressible States –Variety and Universality–

Masatoshi Imada

Published Aug 15, 1994• 25 citations
Publisher

Abstract

Critical properties of transitions between a variety of quantum fluids and the Mott insulator are examined in terms of the transition to an incompressible state. In one dimension, they show universally common properties each other irrespective of the statistics, components and the interaction of particles. In two dimensions, they show qualitative differences originated from the differences in the nature of the quantum fluid. It is useful to categorize the singularity at the Mott transition into two types, namely, one characterized by the charge mass divergence and the other by the vanishment of the carrier number. This difference originates from the number of components. Its variety is further explored by examining various cases such as strongly correlated fermions, hard core bosons and boson t - J models. Critical properties to other incompressible states such as spin gap states and the fractional quantum Hall state are also discussed from the same viewpoint. Relevance of our analyses to the understanding of normal state properties in high- T c cuprates and other transition metal oxides is discussed.

DOI
10.1143/jpsj.63.3059

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Critical properties of transitions between a variety of quantum fluids and the Mott insulator are examined in terms of the transition to an incompressible state. In one dimension, they show universally common properties each other irrespective of the statistics, components and the interaction of particles. In two dimensions, they show qualitative differences originated from the differences in the nature of the quantum fluid. It is useful to categorize the singularity at the Mott transition into two types, namely, one characterized by the charge mass divergence and the other by the vanishment of the carrier number. This difference originates from the number of components. Its variety is further explored by examining various cases such as strongly correlated fermions, hard core bosons and boson t - J models. Critical properties to other incompressible states such as spin gap states and the fractional quantum Hall state are also discussed from the same viewpoint. Relevance of our analyses to the understanding of normal state properties in high- T c cuprates and other transition metal oxides is discussed.
Critical properties of the transition between the Mott insulator and quantum fluids are investigated by using the scaling theory. The Mott insulating phase and the quantum fluid phase of bi-component systems are categorized into several types depending on the existence of order and the type of excitation spectra. The critical exponents of the transition in multicomponent systems are discussed for various combinations of metal-insulator and superfluid-insulator transitions. For the generic transition between a genuinely multicomponent metal and the Mott insulator in d dimensions, the hyperscaling is satisfied with the correlation exponent ν=1/2 d , the dynamical exponent z =2 d , and the Drude weight exponent ζ=32−1d\zeta =\frac32-\frac1dζ=23​−d1​. It is argued that the upper critical dimension d c satisfies d c ≥2. The above exponents are compared with ν=1/2, z =2, and ζ=d2\zeta =\frac{d}2ζ=2d​ for the transition to the band insulator. Critical properties of the energy gap, the compressibility and other quantities are also discussed.
Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.
One type of Mott transition (MT1) is characterized by diverging enhancement of the charge effective mass when one approaches a Mott insulator from the side of the paramagnetic metal. Another fundamentally different type of Mott transition (MT2) is shown to exist when a spin gap opens. The linear coefficient of the specific heat γ decreases and then vanishes at the transition point of MT2 in sharp contrast with MT1. As an example, a dimerized t - J model is shown to undergo MT2. The underlying pairing mechanism determines the character of MT2. Recent controversial experimental results on the Mott transitions in copper oxides and other strongly correlated systems are discussed from the above viewpoint.
We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field, which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics \ensuremath{\alpha}, which can vary between fermions, \ensuremath{\alpha}=0, and bosons, \ensuremath{\alpha}=1. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the fermion limit, the transition is described by a massless 2+1 Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in \ensuremath{\alpha}, and also a large-N expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calculations at and near the boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties that vary continuously and monotonically as one passes from fermions to bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic-field-tuned superconductor-insulator transition are briefly discussed.
Introduction In this chapter we study metal–insulator transitions which occur due to correlations between the charge carriers. This quantum phase transitions results from the competition between kinetic energy and Coulomb repulsion where the latter has the tendency to localise the electrons. The simplest model which describes this competition is the one-band Hubbard model with its two energy scales, the bandwidth W and the Coulomb repulsion U between electrons of opposite spins on the same site. For a fixed density of electrons, n = 1; as the ratio U/W increases, we expect to find a zero-temperature phase transition from a metallic state to an insulator where the electrons are frozen at the lattice sites. The method employed here to investigate this transition is the Gutzwiller approach (Gutzwiller, 1965). This is a variational method which played an important role in providing a framework for the ideas of Mott on the problem of the metal–insulator transition (Mott, 1974). On the metallic side of the transition, this approach describes a metal with renormalised Fermi liquid parameters, essentially with enhanced effective mass and uniform susceptibility. This is the so-called highly correlated electron gas (Brinkman and Rice, 1970) for which the metal oxide V 2 O 3 is the prototype system. In the insulating side, Gutzwiller's approximation yields a noninteracting system of localised electrons. This insulating phase is incompressible , i.e. has zero compressibility and infinite zero temperature susceptibility. The latter is not a consequence of interactions but simply due to the divergence of the Curie susceptibility, χ ∝ 1 /T , of non-interacting moments at T = 0. Then, in Gutzwiller's approach the transition is from a paramagnetic metal to a paramagnetic insulator. We will continue using the designation Mott transition to describe this type of phase transition where the insulating phase has no long-range magnetic order. In real systems, most frequently, localisation due to interactions is accompanied by the appearance of antiferromagnetic order.
Transitions between the Mott insulator and metals in clean systems are analyzed with the scaling theory in terms of quantum critical phenomena. In the case of generic transitions controlled by the filling, the scaling theory is established from analyses of the Drude weight and the compressibility based on hyperscaling. In the transition to the Mott insulator, a new universality class with the correlation length exponent ν<1/2 and the dynamical exponent z >2 is derived, which is in contrast to the transition to the band insulator characterized by ν=1/2 and z =2. The unusual exponents lead to various anomalous characters of metals near the Mott insulator such as strong suppression of the degeneracy temperature, and nonlinear dependence of the Drude weight on the doping concentration. Remarkable properties are also found in the specific heat, the compressibility and spin correlations. A mechanism of high temperature superconductivity is discussed in terms of the release from the suppressed coherence.