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(T, δU ) = ρc(T )f (T /To(δU )), with To(δU ) ∼ |δU | zν , and ρc(T ) ∼ T . The corresponding β-function displays a "strong coupling" form β ∼ ln(ρc/ρ), reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.

The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of quantum Widom lines and present a detailed discussion that highlights its physical meaning when used in the context of quantum phase transitions.

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 transition are confined to extremely low temperatures, while clear signatures of Mott quantum criticality emerge across much of the phase diagram. Remarkable scaling behavior is identified for the entire family of resistivity curves, with a quantum critical region covering the entire BM regime, providing not only insight, but also quantitative understanding around the MIR limit, in agreement with the available experiments.PACS numbers: 71.27.+a,71.30.+h Metallic transport inconsistent with Fermi liquid theory has been observed in many different systems; it is often linked to quantum criticality around some ordering phase transition [1, 2]. Such behavior is notable near quantum critical points in good conductors, for example in heavy fermion compounds [3, 4]. In several other classes of materials, however, much more dramatic departures form conventional metallic behavior are clearly observed, where resistivity still rises linearly with temperature, but it reaches paradoxically large values, well past the MIR limit [5, 6]. This "Bad-Metal" (BM) behavior [7], was first identified in the heyday of high-temperature superconductivity, in materials such as La 2−x Sr x CuO 4 [8]. While the specific copper-oxide family and related high-T c materials remain ill-understood and marred with controversy, it soon became clear that BM behavior is a much more general feature [6] of materials close to the Mott metal-insulator transition (MIT) [9]. Indeed, it has been clearly identified also in various oxides [10, 11], organic Mott systems [12][13][14], as well as more recently discovered families of iron pnictides [15]. Despite years of speculation and debate, so far its clear physical interpretation has not been established.To gain reliable insight into the origin of BM behavior, it is useful to examine an exactly solvable model system, where one can suppress all possible effect associated with the approach to some broken symmetry phase, or those specific to low dimensions and a given lattice structure. This can be achieved by focusing on the "maximally frustrated Hubbard model", where an exact solution can be obtained by solving Dynamical Mean-Field Theory (DMFT) equations [16] in the paramagnetic phase. Although various aspects of the DMFT equation have been studied for more than twenty years, only very recent work [17,18] established how to identify the quantum critical (QC) behavior associated with the interaction-driven Mott transition at ...

The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible vertex function Γ have revealed an inherent limitation of this approach. Here we demonstrate how these undesirable properties of the LWF can lead to a failure of computational methods based on an approximation of the LWF. We apply the Nested Cluster Scheme (NCS) to the Hubbard model and observe the existence of an additional stationary point of the self-consistent equations, associated with an unphysical branch of the LWF. In the strongly correlated regime, starting with the first divergence of Γ, this unphysical stationary point becomes attractive in the standard iterative technique used to solve DMFT. This leads to an incorrect solution, even in the large cluster size limit, for which we discuss diagnostics. arXiv:1709.10490v3 [cond-mat.str-el]

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results and the question of the exact solution for the conductivity in the Hubbard model remained open. In this letter we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity, and identify the best available result to be compared to experiment. We find that at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4 × 4 and the corresponding Lanczos diagonalization result is therefore close to the exact result in the thermodynamic limit. arXiv:1811.08343v4 [cond-mat.str-el]

We present an embedded-cluster method, based on the TRILEX formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, selfenergies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW +extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.Two major approaches have been put forth to fathom the nature of high-temperature superconductivity. Spin fluctuation theory [1][2][3][4][5][6][7][8] , inspired by the early experiments on cuprate compounds, is based on the introduction of phenomenological bosonic fluctuations coupled to the electrons. It belongs to a larger class of methods, including the fluctuation-exchange (FLEX) 9 and GW approximations 10,11 , or the Eliashberg theory of superconductivity 12 . In the Hubbard model, these methods can formally be obtained by decoupling the electronic interactions with Hubbard-Stratonovich (HS) bosons carrying charge, spin or pairing fluctuations. They are particularly well suited for describing the system's long-range modes. However, they suffer from two main drawbacks: without an analog of Migdal's theorem for spin fluctuations, they are quantitatively uncontrolled; worse, the results depend on the precise form of the bosonic fluctuations used to decouple the interaction term, an issue referred to as the "Fierz ambiguity" [13][14][15][16][17][18] .A second class of methods, following Anderson 19 , puts primary emphasis on the fact that the undoped compounds are Mott insulators, where local physics plays a central role. Approaches like dynamical mean field theory (DMFT) 20 and its cluster extensions 21-25 , which self-consistently map the lattice problem onto an effective problem describing a cluster of interacting atoms embedded in a noninteracting host, are tools of choice to examine Anderson's idea. Cluster DMFT has indeed been shown to give a consistent qualitative picture of cuprate physics, including pseudogap and superconducting phases . Compared to fluctuation theories, it a priori comes with a control parameter, the size N c of the embedded cluster. However, this is of limited practical use, since the convergence with N c is nonmonotonic for small N c 33 , requiring large N c 's, which cann...

We study Cooper pairing in the Dirac composite fermion (CF) system. The presence of the mass term in the Dirac CF description (which may simulate Landau level mixing) i.e. breaking of particle-hole (PH) symmetry in this system, is a necessary condition for the existence of a PH Pfaffian-like topological state. In the scope of RPA approximation and hydrodynamic approach, we find some signatures of pairing at finite frequencies. Motivated by this insight, we extend our analysis to the case of a different but still Dirac quasi-particle (CF) representation, appropriate in the presence of a mass term, and discuss the likelihood of PH Pfaffian pairing and Pfaffian pairing in general. On the basis of gauge field effects, we find for small Dirac mass anti-Pfaffian or Pfaffian instability depending on the sign of mass, while for large mass (Landau level mixing), irrespective of its sign, PH Pfaffian-like instability.

The interplay between Mott and Anderson routes to localization in disordered interacting systems gives rise to different transitions and transport regimes. Here, we investigate the phase diagram at finite temperatures using dynamical mean field theory combined with typical medium theory, which is an effective theory of the Mott-Anderson metal-insulator transition. We mainly focus on the properties of the coexistence region associated with the Mott phase transition. For weak disorder, the coexistence region is found to be similar as in the clean case. However, as we increase disorder Anderson localization effects are responsible for shrinking the coexistence region and at sufficiently strong disorder (approximately equal to twice the bare bandwidth) it drastically narrows, the critical temperature abruptly goes to zero, and we observe a phase transition in the absence of a coexistence of the metallic and insulating phases. In this regime, the effects of interaction and disorder are found to be of comparable importance for charge localization.Comment: minor changes, 8 pages, 9 figure