Anomalous Quantum Criticality Achieves Novel Insights into 2-Site Falicov-Kimball Models

Researchers have long sought to understand the complex behaviour arising at continuous metal-insulator transitions, particularly the elusive nature of quantum criticality. M. S. Laad and Prosenjit Haldar, from the Department of Physics at the National Institute of Technology Agartala, alongside et al., now present a fully analytic theory addressing this challenge within the well-established Falicov-Kimball model. Their work, focused on a hierarchical Cayley tree structure, reveals anomalous dimensions in density fluctuation modes and uncovers a surprising collapse of a ‘sub-diffusive’ metallic state to a single point , the Mott-like quantum critical point , at least on the Bethe lattice. This breakthrough provides crucial microscopic insight into Mott-like criticality, offering a deeper understanding of thermal and dynamical responses in numerous physical systems effectively described by the Falicov-Kimball model.

Falicov-Kimball Model and Bethe Lattice Criticality represent important

Scientists have demonstrated a fully analytic theory for Mott-like quantum criticality within the Falicov-Kimball model (FKM) on a hierarchical Cayley tree, also known as a Bethe lattice. This breakthrough reveals insights into the microscopic processes driving novel critical behaviour in correlated fermion systems, an area where analytic understanding has remained scarce despite extensive numerical studies. The team achieved this by utilising a single input from a 2-site cluster-dynamical mean-field theory (CDMFT), allowing them to map out the behaviour of density fluctuation modes and uncover anomalous dimensions originating from infra-red power-law singular cluster self-energies. Interestingly, the research establishes that a sub-diffusive metal exhibiting glassy dynamics, previously separating a weakly ergodic metal from a non-ergodic insulator, collapses to a single point, the Mott-like quantum critical point, at least within the Bethe lattice framework.
Experiments show that density fluctuation modes acquire anomalous dimensions, a key finding stemming from the infra-red power-law singular cluster self-energies identified by the researchers. This anomalous behaviour is particularly significant at zero temperature, where the sub-diffusive metal with glassy dynamics, previously observed to exist between metallic and insulating phases, shrinks to a single point defining the Mott-like quantum critical point on the Bethe lattice. The study unveils that this critical point is associated with a continuous metal-insulator transition, a phenomenon crucial for understanding strongly correlated electron systems. By employing a 2-site CDMFT, the scientists were able to develop a fully analytic theory, providing a level of detail previously unattainable through numerical methods alone.

The research details the consequences of this anomalous criticality for a range of thermal and dynamical responses, offering potential implications for various physical systems effectively modelled by the FKM.The FKM, long recognised as the simplest model of correlated fermions exhibiting a Mott-like critical point, is also isomorphic to an annealed binary-alloy disorder model, further broadening the applicability of these findings. This work opens avenues for understanding the behaviour of materials undergoing correlation-driven metal-insulator transitions, phenomena underpinning the anomalous physical responses of strongly correlated electron systems. The team’s approach provides a foundation for investigating the elusive quantum-critical nature of the metal-insulator transition and exploring the emergence of anomalous metallic states without conventional Landau Fermi liquid quasiparticles.

Bethe Lattice Analysis of Mott-Like Criticality reveals novel

Scientists developed a fully analytic theory to investigate Mott-like criticality within the Falicov-Kimball model (FKM) using a hierarchical Cayley tree, or Bethe lattice. This work addresses a long-standing gap in understanding the microscopic origins of this novel Mott-like critical point, despite extensive numerical investigations of the FKM. The research team harnessed a single input derived from a 2-site cluster-dynamical mean-field theory (CDMFT) to construct their analytic framework, enabling detailed examination of the system’s behaviour. Experiments employed a Bethe lattice configuration to model the FKM, allowing the team to analyse density fluctuation modes and reveal anomalous dimensions arising from infra-red power-law singular cluster self-energies.

This innovative approach uncovered that a sub-diffusive metallic state, characterised by glassy dynamics, collapses to a single point, the Mott-like quantum critical point, at least within the Bethe lattice structure. The study pioneered a method for calculating these critical behaviours analytically, a significant advancement over previous predominantly numerical approaches. Researchers detailed the consequences of this anomalous criticality for both thermal and dynamical responses, extending the applicability of the findings to a range of physical systems effectively modelled by the FKM. The team observed Mooij correlations, evidenced by a negative derivative of density with respect to temperature over an extended temperature range, mirroring previous CDMFT work and reinforcing the model’s validity.

This analytical approach allows direct application to systems exhibiting similar correlations, such as those found in certain disordered materials. Furthermore, the study demonstrated that the developed methodology is applicable to systems where itinerant fermions are strongly coupled to Ising variables, potentially offering insights into the “Quantum disentangled liquid” (QDL) phase and (Z2) Ising gauge theories.The system delivers a non-ergodic, subdiffusive QDL state only at the Mott-like QCP, separating an ergodic metal from a non-ergodic insulator, a crucial finding for understanding complex quantum phenomena. This work establishes a powerful theoretical foundation for exploring correlated electron systems and their emergent properties.

Falicov-Kimball Model Reveals Novel Critical Point in Correlated

Scientists have uncovered a novel Mott-like critical point (QCP) within the Falicov-Kimball model (FKM), a simplified representation of correlated fermions exhibiting a continuous metal-insulator transition (MIT). The research details a fully analytic theory for this criticality on a hierarchical Cayley tree, utilising insights from a 2-site cluster-dynamical mean-field theory (CDMFT). Experiments revealed that density fluctuation modes acquire anomalous dimensions, stemming from infra-red power-law singular cluster self-energies, a key0.8, with ν = 0.36. Measurements confirm that ImΣc(ω) scales as |ω|α, with α = 1/3 at the Mott-like MIT, leading to a quasiparticle residue zc(ω) proportional to ω1−α.

Results demonstrate that this anomalous criticality profoundly impacts thermal and dynamical responses in physical systems effectively modelled by the FKM. The study details how the singular fermion self-energies at the MIT directly induce infra-red singular vertices, drastically modifying the charge fluctuation spectrum, quantified by χch(q, ω) ≃ 1/ω, and introducing a branch-point singularity in the diffusion propagator. Tests prove that the memory function, M(q, ω), exhibits anomalous behaviour at the Mott QCP, scaling as M(q, ω) ≃ ω−(1−2α), revealing an infra-red singular branch-cut form. Furthermore, the research establishes that doping the system with a small number of magnetic impurities transforms it into a lattice version of a power-law pseudogap Kondo impurity model. Scientists recorded that the local moment amplitude, Mloc, scales as (Jc −J)β for J.