The Mott critical point between a metal and a correlated insulator has usually been studied via density or spin density bosonic mode fluctuations according to the standard Ginzburg-Landau-Wilson phase transition paradigm. A moment's reflection leads to increasing doubts that such an approach should work as the transition is nonmagnetic, voiding the relevance of spin density modes. Charge density modes are irrelevelant since the long range Coulomb interaction leads to a large plasmon gap and their incompressibility. In solidarity with these doubts, recent measurements of the Mott critical point in low dimensional organic materials yield critical exponents in violent diasagreement with the bosonic mode criticality lore. We propose that fermionic fluctuations control the behavior of the Mott transition. The transition thus has an intrinsic quantum aspect despite being a finite temperature phase transition. We develop this hitherto unexplored physics, obtain experimental predictions and find agreement with one of the novel unexplained experimental exponents. We conclude that this Mott transition corresponds to a new universality class of finite temperature critical points that contains quantum effects and cannot be accounted for by conventional Ginzburg-Landau-Wilson wisdom.
Hall coefficient implies the mechanism for reconstruction of a Fermi surface, distinguishing competing scenarios for Mott criticality such as electron fractionalization, dynamical mean-field theory, and metal-insulator transition driven by symmetry breaking. We find that electron fractionalization leaves a signature for the Hall coefficient at Mott criticality in two dimensions, a unique feature differentiated from other theories. We evaluate the Hall coefficient based on the quantum Boltzman equation approach, guaranteeing gauge invariance in both longitudinal and transverse transport coeffic…
Experiments performed over the last twenty years have revealed striking similarities between several two-dimensional (2D) fermion systems, including diluted two-dimensional electron liquids in semiconductors, 3He monolayers, and layered organic charge-transfer salts. These experimental results, together with recent theoretical advances, provide compelling evidence that strong electronic correlations - Wigner-Mott physics - dominate the universal features of the corresponding metal-insulator transitions (MIT). Here we review the recent theoretical work exploring quantum criticality of Mott and …
Bad-Metal (BM) behavior featuring linear temperature dependence of the resistivity extending to well above the Mott-Ioffe-Regel (MIR) limit is often viewed as one of the key unresolved signatures of strong correlation. Here we associate the BM behavior with the Mott quantum criticality by examining a fully frustrated Hubbard model where all long-range magnetic orders are suppressed, and the Mott problem can be rigorously solved through Dynamical Mean-Field Theory. We show that for the doped Mott insulator regime, the coexistence dome and the associated first-order Mott metal-insulator transiti…
In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner--Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at t…
Electrons undergoing a Mott transition may shed their charge but persist as neutral excitations of a quantum spin liquid (QSL). We introduce concrete two-dimensional models exhibiting this exotic behavior as they transition from superconducting or topological phases into fully charge-localized insulators. We study these Mott transitions and the confinement of neutral fermions at a second transition into a symmetry-broken phase. In the process, we also derive coupled-wire parent Hamiltonians for a non-Abelian QSL and a $\mathbb{Z}_4$ QSL.
Unconventional superconductivity typically occurs in materials in which a small change of a parameter such as bandwidth or doping leads to antiferromagnetic or Mott insulating phases. As such competing phases are approached, the properties of the superconductor often become increasingly exotic. For example, in organic superconductors and underdoped high-$T_\mathrm{c}$ cuprate superconductors a fluctuating superconducting state persists to temperatures significantly above $T_\mathrm{c}$. By studying alloys of quasi-two-dimensional organic molecular metals in the $κ$-(BEDT-TTF)$_2$X family, we r…
We study the continuous bandwidth-controlled Mott transition in the two-dimensional single-band Hubbard model with a focus on the critical scaling behavior of charge and spin degrees of freedom. Using plaquette cluster dynamical mean-field theory, we find charge and spin criticality consistent with experimental results for organic conductors. In particular, the charge degree of freedom measured via the local density of states at the Fermi level shows a smoother transition than expected for the Ising universality class and in single-site dynamical mean-field theory, revealing the importance of …
We present evidence for Mott quantum criticality in an anisotropic two-dimensional system of coupled Hubbard chains at half-filling. In this scenario emerging from variational cluster approximation and cluster dynamical mean-field theory, the interchain hopping $t_{\perp}$ acts as a control parameter driving the second-order critical end point $T_c$ of the metal-insulator transition down to zero at $t_{\perp}^{c}/t\simeq 0.2$. Below $t_{\perp}^{c}$, the volume of the hole and electron Fermi pockets of a compensated metal vanishes continuously at the Mott transition. Above $t_{\perp}^{c}$, the …
We study electric transport near the Mott metal-insulator transition in a triangular-lattice Hubbard model at half filling. We calculate optical conductivity $σ(ω)$ based on a cellular dynamical mean field theory including vertex corrections inside the cluster. Near the Mott critical end point, a Drude analysis in the metallic region suggests that the change in the Drude weight is important rather than that in the transport scattering rate for the Mott transition. In the insulating region, there emerges an "ingap" peak in $σ(ω)$ at low $ω$ near the Mott transition, and this smoothly connects t…
Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastab…
Coupling of charge and lattice degrees of freedom in materials can produce intriguing electronic phenomena, such as conventional superconductivity where the electrons are mediated by lattice for creating supercurrent. The Mott transition, which is a source for many fascinating emergent behaviors, is originally thought to be driven solely by correlated electrons with an Ising criticality. Recent studies on the known Mott systems have shown that the lattice degree of freedom is also at play, giving rise to either Landau or unconventional criticality. However, the underlying coupling mechanism of…
The twin issues of the nature of the normal state and competing order(s) in the iron arsenides are central to understanding their unconventional, high-Tc superconductivity. We use a combination of transport anisotropy measurements on detwinned Sr(Fe(1-x)Co(x))2As2 single crystals and local density approximation plus dynamical mean field theory (LDA + DMFT) calculations to revisit these issues. The peculiar resistivity anisotropy and its evolution with x are naturally interpreted in terms of an underlying orbital-selective Mott transition (OSMT) that gaps out the dxz or dyz states. Further, we …
We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wavefunctions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime…
Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as…
The critical properties of the finite temperature Mott endpoint are drastically altered by a coupling to crystal elasticity, i.e., whenever it is amenable to pressure tuning. Similar as for critical piezoelectric ferroelectrics, the Ising criticality of the electronic system is preempted by an isostructural instability, and long-range shear forces suppress microscopic fluctuations. As a result, the endpoint is governed by Landau criticality. Its hallmark is thus a breakdown of Hooke's law of elasticity with a non-linear strain-stress relation characterized by a mean-field exponent. Based on a …
Dynamically driven interacting quantum many-body systems have the potential to exhibit properties that defy the laws of equilibrium statistical mechanics. A widely studied model is the impulsively driven antiferromagnetic Mott insulator, which is predicted to realize exotic transient phenomena including dynamical phase transitions into thermally forbidden states and highly non-thermal magnon distributions. However such far-from-equilibrium regimes, where conventional time-dependent Ginzburg-Landau descriptions fail, are experimentally challenging to prepare and to probe especially in solid sta…
We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\sim 1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.
Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal
Indian Institute of Science Education and Research Kolkata（印度科学教育研究所加尔各答分校）；The Institute of Mathematical Sciences, HBNI（数学科学研究所，HBNI）；National Institute of Science, Education and Research, HBNI（国家科学、教育和研究学院，HBNI）；Jawaharlal Nehru Center for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-…
We forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness as advocated by Phillips and supported by recent DCA results on the Hubbard model is setting the necessary microscopic conditions. The crucial insight is due to Weng who demonstrated that in the presence of Mottness the fundamental workings of quantum statistics changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical meth…
We consider the low-temperature differential tunneling conductance $G$ for interfaces between a planar insulating material in the Mott-class and a metal. For values of the the applied potential difference $V$ that are not very small, there is a experimentally observed universal regime in which $G \sim V^m$, where $m$ is a universal exponent. We consider the theoretical prediction of the values of $m$ by using the method of Effective Field Theory ($EFT$), which is appropriate for discussing universal phenomena. We describe the Mott material by the $EFT$ pertaining the long-distance behavior of …
We use quantum Monte Carlo simulations to study a disordered S=1/2 Heisenberg quantum spin model with three different nearest-neighbor interactions, J1<=J2<=J3, on the square lattice. We consider the regime in which J1 represents weak bonds, and J2 and J3 correspond to two kinds of stronger bonds (dimers) which are randomly distributed on columns forming coupled 2-leg ladders. When increasing the average intra-dimer coupling (J2+J3)/2, the system undergoes a Neel to quantum glass transition of the ground state and later a second transition into a quantum paramagnet. The quantum glass phase is …
Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system V_2O_3
We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to topological insulator (TI) or Chern insulator (CI). Changes in Fermi surface topology concomitant with (SU(2) or time reversal) symmetry breakings generate quantum critical lines (QCL) even beyond the quantum critical point. This QCL running at temperature $T=0$ separates two distinct topological phases. This is in contrast to the simple termination of the finite temperature critical line at the quantum critical poi…
Recent experiments have discovered multipolar orders in a variety of $d$-orbital Mott insulators. Motivated by uncovering the exchange interactions which underlie octupolar order proposed in the osmate double perovskites, we study a two-site model using exact diagonalization on a five-orbital Hamiltonian, incorporating spin-orbit coupling (SOC) and interactions, and including both intra-orbital and inter-orbital hopping. Using an exact Schrieffer-Wolff transformation, we then extract an effective pseudospin Hamiltonian for the non-Kramers doublets, uncovering dominant ferrooctupolar coupling d…
In the field of interacting electron systems the Mott metal-to-insulator (MI) transition represents one of the pivotal issues. The role played by lattice degrees of freedom for the Mott MI transition and the Mott criticality in a variety of materials are current topics under debate. In this context, molecular conductors of the $κ$-(BEDT-TTF)$_2$X type constitute a class of materials for unraveling several aspects of the Mott physics. In this review, we present a synopsis of literature results with focus on recent expansivity measurements probing the Mott MI transition in this class of material…
Anomalous Quantum Criticality at a Continuous Metal-Insulator Transition
The Institute of Mathematical Sciences（马图拉科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Department of Physics, National Institute of Technology Agartala（阿格塔拉国立理工学院物理系）
We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in presence of Hund's coupling interaction. By analytical analysis of Hamiltonian, we show that the locking of the two orbitals vs.\,orbital-selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean-field to impurity problem, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the sla…
Moiré bilayer materials have recently attracted much attention following the discovery of various correlated insulating states at specific band fillings. Here we discuss the metal-insulator transitions (MITs) that have been observed in the same devices, but at fillings far from the strongly correlated regime dominated by Mott-like physics, displaying many similarities to other examples of disorder-dominated MITs. We propose a minimal theoretical model describing the interplay of interactions and disorder, which able to capture most experimental trends observed on several devices.
We report the first application of critical cluster techniques to the Mott metal-insulator transition in vanadium dioxide. We show that the geometric properties of the metallic and insulating puddles observed by scanning near-field infrared microscopy are consistent with the system passing near criticality of the random field Ising model as temperature is varied. The resulting large barriers to equilibrium may be the source of the unusually robust hysteresis phenomena associated with the metal-insulator transition in this system.
We study electric transport near the Mott metal-insulator transition. Optical conductivity of the half-filled Hubbard model on a triangular lattice is calculated based on a cellular dynamical mean field theory including vertex corrections inside the cluster. By investigating the spectrum at low frequencies, we find that a Drude peak on the metallic side smoothly connects to an "ingap" peak on the insulating side. The optical weight of these peaks exhibits a critical behavior with power-law near the Mott critical end point, $|D-D^*|\propto|U-U^*|^{1/δ}$. We find that the critical exponent $1/δ$…
We study critical singularities in the d-wave-like superconducting phase of the hole-doped Hubbard model of repulsively interacting electrons, defined on a two-leg ladder, induced by a magnetic field applied parallel to the ladder plane. We argue that, provided the lowest energy spin excitations in doped ladders carry as well charge quantum numbers, the low temperature thermodynamic quantities, such as specific heat coefficient and magnetic susceptibility will show logarithmic singularities in quantum critical regime. This behavior is in drastic contrast with the magnetic field induced critica…
The fate of exotic spin liquid states with fractionalized excitations at finite temperature ($T$) is of great interest, since signatures of fractionalization manifest in finite-temperature ($T$) dynamics in real systems, above the tiny magnetic ordering scales. Here, we study a Jordan-Wigner fermionized Kitaev spin liquid at finite $T$ employing combined Exact diagonalization and Monte Carlo simulation methods. We uncover $(i)$ checkerboard or stripy-ordered flux crystals depending on density of flux, and $(ii)$ establish, surprisingly, that: $(a)$ the finite-$T$ version of the $T=0$ transitio…
Ginzburg-Landau theory describes phase transitions as the competition between energy and entropy: The ordered phase has lower energy, while the disordered phase has larger entropy. When heating the system, ordering is reduced entropically until it vanishes at the critical temperature. This established picture implicitly assumes that the energy difference between ordered and disordered phase does not change with temperature. We show that for the Mott insulator KCuF3 this assumption is strongly violated: thermal expansion energetically stabilizes the orbitally-ordered phase to such and extent th…
Motivated by the recent activities on the Ni-based diamond lattice antiferromagnet NiRh$_2$O$_4$, we theoretically explore on a general ground the unique spin and orbital physics for the Ni$^{2+}$ ions with a $3d^8$ electron configuration in the tetrahedral crystal field environment and on a diamond lattice Mott insulator. The superexchange interaction between the local moments usually favors magnetic orders. Due to the particular electron configuration of the Ni$^{2+}$ ion with a partially filled upper $t_{2g}$ level and a fully filled lower $e_g$ level, the atomic spin-orbit coupling becomes…
Quantum phase transitions in metals are often accompanied by violations of Fermi liquid behavior in the quantum critical regime. Particularly fascinating are transitions beyond the Landau-Ginzburg-Wilson concept of a local order parameter. The breakdown of the Kondo effect in heavy-fermion metals constitutes a prime example of such a transition. Here, the strongly correlated f electrons become localized and disappear from the Fermi surface, implying that the transition is equivalent to an orbital-selective Mott transition, as has been discussed for multi-band transition-metal oxides. In this a…
We perform a systematic study of incoherent transport in the high temperature crossover region of the half-filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form $ρ(δU,T)=ρ_{c}(T)f(T/T_{o}(δU))$, with $T_{o}(δU)\simδU^{zν}$, and $ρ_{c}(T)\sim T$. The corresponding $β$-function displays a "strong coupling" form $β\sim\ln(ρ_{c}/ρ)$, reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticalit…
We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This …
