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A new bosonic, excitonic method for interacting electrons is developed. For two-dimensional electron liquid, it reveals a noncompensated quantum crystal phase ranging from the high density, or vanishing Coulomb interaction, limit: $r_s=0$,…
Recent progresses using state-of-the-art experimental techniques have motivated a number of new insights on heavy fermion physics. This article gives a brief summary of the author's research along this direction. We discuss five major…
We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical non-linear $\sigma$ model of the quantum ferrimagnets at zero temperature…
We review the latest developments in the field of the metal-insulator transition in strongly-correlated two-dimensional electron systems. Particular attention is given to recent discoveries of a sliding quantum electron solid and…
Landau Fermi liquid theory is a fixed point theory of metals that includes the forward scattering amplitudes as exact marginal couplings. However, the fixed point theory that only includes the strict forward scatterings is non-local in real…
Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal-insulator transition. We investigate the Mott transition in a Hubbard model by…
We study phase transitions driven by fermionic double-trace deformations in gauge-gravity duality. Both the strength of the double trace deformation and the infrared conformal dimension/self-energy scaling of the quasiparticle can be used…
We present a general approach to understanding the quantum phases and phase transitions of quantum antiferromagnets in two spatial dimensions. We begin with the simplest spin liquid state, the Z_2 spin liquid, whose elementary excitations…
It has been claimed that an impurity hopping between two sites in a metal can lead to non--Fermi liquid behavior if the bias between the two sites is tuned to zero. Here it is shown that several extra tunnelling processes are allowed; those…
The behavior of the electronic system of heavy fermion metals is considered. We show that there exist at least two main types of the behavior when the system is nearby a quantum critical point which can be identified as the fermion…
Superfluidity of spatially separated electrons and holes and unbalanced two-layer electron system in high magnetic field is considered. The temperature of the Kosterlitz-Thouless transition to a superfluid state is obtained as a function of…
We show that thermodynamics is insufficient to probe the nature of the low energy dynamics of quantum impurity models and a more subtle analysis based on scattering theory is required. Traditionally, quantum impurity models are classified…
Using recent insights obtained in heavy fermion physics on the thermodynamic singularity structure associated with quantum phase transitions, we present here an experimental strategy to establish if the zero-temperature transition in the…
A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention…
In this overview we provide a general introduction to metal-insulator transitions, with focus on specific mechanisms that can localize the electrons in absence of magnetic or charge ordering, and produce well defined quantum critical…
In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system…
Solid atomic hydrogen is one of the simplest systems to undergo a metal-insulator transition. Near the transition, the electronic degrees of freedom become strongly correlated and their description provides a difficult challenge for…
Quantum criticality of metal-insulator transitions in correlated electron systems is shownto belong to an unconventional universality class with violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry breaking transitions.…
One of the greatest challenges to Landau's Fermi liquid theory - the standard theory of metals - is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic…
Superconductor-insulator transition is one of the remarkable phenomena driven by quantum fluctuation in two-dimensional (2D) systems. Such a quantum phase transition (QPT) was investigated predominantly on highly disordered thin films with…