Several years ago, there were rumors that metals might have an awkward cousin, whom people are sort of expecting but have never made acquaintance. As though he/she shares metallic features -- conducting -- but is distinctively different and even invisible if one approaches him/her in conventional manners -- acquiring no Fermi surface or quasiparticles. Of course, the real content of such metaphor ammounts to the fact that there exists new quantum metallic state that conducts electricity but is orthogonal to the established paradigm of Landau's Fermi-liquid (FL), and such state might hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL -- dubbed non-Fermi-liquid (nFL) -- ranging from the Cu- and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to realize such exotic state of matter, at least theoretically, one would need to construct a lattice model and solve it with unbiased quantum many-body machinery. Here, we achieve this goal by designing a 2D lattice model comprised of matter fields coupled with dynamic Z2 gauge fields, and studying it with sign-free quantum Monte Carlo simulations. We find as the bosonic matter fields become disordered, the system reacts with changing its nature from the conventional normal metal of FL with proper Fermi surface to an orthogonal metal of nFL without Fermi surface and quasiparticle and yet still responds to external perturbation with hidden fermionic degrees of freedom. Such a quantum phase transition from a normal metal to an orthogonal metal has never been seen before and certainly violated the Luttinger's theorem. These results are calling for the establishment of new paradigm of quantum metals and their transition with conventional ones. Rumor turns out to be true, as always, that metals indeed have an awkaward cousin.
Several years ago, there were rumors that metals might have an awkward cousin, whom people are sort of expecting but have never made acquaintance. As though he/she shares metallic features -- conducting -- but is distinctively different and even invisible if one approaches him/her in conventional manners -- acquiring no Fermi surface or quasiparticles. Of course, the real content of such metaphor ammounts to the fact that there exists new quantum metallic state that conducts electricity but is orthogonal to the established paradigm of Landau's Fermi-liquid (FL), and such state might hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL -- dubbed non-Fermi-liquid (nFL) -- ranging from the Cu- and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to realize such exotic state of matter, at least theoretically, one would need to construct a lattice model and solve it with unbiased quantum many-body machinery. Here, we achieve this goal by designing a 2D lattice model comprised of matter fields coupled with dynamic Z2 gauge fields, and studying it with sign-free quantum Monte Carlo simulations. We find as the bosonic matter fields become disordered, the system reacts with changing its nature from the conventional normal metal of FL with proper Fermi surface to an orthogonal metal of nFL without Fermi surface and quasiparticle and yet still responds to external perturbation with hidden fermionic degrees of freedom. Such a quantum phase transition from a normal metal to an orthogonal metal has never been seen before and certainly violated the Luttinger's theorem. These results are calling for the establishment of new paradigm of quantum metals and their transition with conventional ones. Rumor turns out to be true, as always, that metals indeed have an awkaward cousin.
Orthogonal metal is a new quantum metallic state that conducts electricity but acquires no Fermi surface (FS) or quasiparticles, and hence orthogonal to the established paradigm of Landau’s Fermi-liquid (FL). Such a state may hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL, i.e., dubbed non-Fermi-liquid (nFL), ranging from the Cu- and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to fully understand such an exotic state of matter, at least theoretically, one would like to construct a lattice model and to solve it with unbiased quantum many-body machinery. Here we achieve this goal by designing a 2D lattice model comprised of fermionic and bosonic matter fields coupled with dynamic ℤ2 gauge fields, and obtain its exact properties with sign-free quantum Monte Carlo simulations. We find that as the bosonic matter fields become disordered, with the help of deconfinement of the ℤ2 gauge fields, the system reacts with changing its nature from the conventional normal metal with an FS to an orthogonal metal of nFL without FS and quasiparticles and yet still responds to magnetic probe like an FL. Such a quantum phase transition from a normal metal to an orthogonal metal, with its electronic and magnetic spectral properties revealed, is calling for the establishment of new paradigm of quantum metals and their transition with conventional ones.
A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.
Since the discovery of the pseudogap and Fermi arc states in underdoped cuprates, the understanding of such non-Fermi-liquid states and the associated violation of Luttinger's theorem have been the central theme in correlated electron systems. However, still lacking is a well-accepted theoretical framework to unambiguously explain these metallic states that are clearly beyond Landau's Fermi liquid and Luttinger's theorem of a Fermi surface and electron filling. Here, we design a lattice model of orthogonal metals with fermion and Ising matter fields coupled to topological order and, by solving the model via unbiased quantum Monte Carlo simulation at generic electron fillings, find that the system gives birth to phenomena of the Fermi arc and pseudogap in the single-particle spectrum that go beyond the Luttinger sum rule with broken Fermi surface but no symmetry breaking. The pseudogap and Fermi arcs coexist with a background of a deconfined Z2 gauge field, and we further find that the confinement transition of the gauge field triggers a superconductivity instability and that the hopping of the gauge-neutral fermions brings the ``large'' Fermi surface back from the Fermi arc state. Our unbiased numerical results provide a concrete model realization and theoretical framework for the coupling between gauge field and fermions and, in the process, generate the rich phenomena of the pseudogap, the Fermi arc, and superconductivity in generic correlated electron systems.
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.
The paradigm of Landau Fermi liquid theory has successfully described the low-energy behavior of numerous metallic systems. However, a growing number of experimental observations in strongly correlated electron materials, such as high-temperature superconductors and heavy fermion compounds, defy this conventional description, exhibiting what is known as non-Fermi liquid (NFL) behavior. These exotic states lack well-defined quasiparticle excitations, displaying anomalous scaling laws and transport properties. Ultracold atomic gases have emerged as highly controllable quantum simulators for strongly correlated matter, offering unprecedented access to tunable interaction strengths, dimensionality, and lattice geometries. This paper explores the potential of ultracold fermionic gases to unveil and characterize NFL behavior. We review the theoretical underpinnings of Landau Fermi liquid theory and its breakdown, survey prominent theoretical models for NFL states, and highlight experimental techniques in ultracold atomic systems pertinent to their detection. Specific attention is given to phenomena such as the BCS-BEC crossover, quantum criticality, and pseudogap phases in ultracold fermions, where strong interactions are expected to lead to deviations from quasiparticle descriptions. We discuss experimental signatures like anomalous spectral functions, linear-in-temperature resistivity analogs, and deviations in thermodynamic properties, proposing how these could be observed and analyzed in current and future ultracold atom platforms. This research aims to leverage the purity and tunability of atomic gases to gain fundamental insights into the nature of NFL states, contributing to a broader understanding of quantum many-body physics beyond the conventional quasiparticle picture.
Experiments on strongly correlated quasi-two-dimensional electronic materials---for example, the high-temperature cuprate superconductors and the putative quantum spin liquids kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2---routinely reveal highly mysterious quantum behavior which cannot be explained in terms of weakly interacting degrees of freedom. Theoretical progress thus requires the introduction of completely new concepts and machinery beyond the traditional framework of the band theory of solids and its interacting counterpart, Landau's Fermi liquid theory. In full two dimensions, controlled and reliable analytical approaches to such problems are severely lacking, as are numerical simulations of even the simplest of model Hamiltonians due to the infamous fermionic sign problem.Here, we attempt to circumvent some of these difficulties by studying analogous problems in quasi-one dimension. In this lower dimensional setting, theoretical and numerical tractability are on much stronger footing due to the methods of bosonization and the density matrix renormalization group, respectively. Using these techniques, we attack two problems: (1) the Mott transition between a Fermi liquid metal and a quantum spin liquid as potentially directly relevant to the organic compounds kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2 and (2) non-Fermi liquid metals as strongly motivated by the strange metal phase observed in the cuprates. In both cases, we are able to realize highly exotic quantum phases as ground states of reasonable microscopic models. This lends strong credence to respective underlying slave-particle descriptions of the low-energy physics, which are inherently strongly interacting and also unconventional in comparison to weakly interacting alternatives.Finally, working in two dimensions directly, we propose a new slave-particle theory which explains in a universal way many of the intriguing experimental results of the triangular lattice organic spin liquid candidates kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. With use of large-scale variational Monte Carlo calculations, we show that this new state has very competitive trial energy in an effective spin model thought to describe the essential features of the real materials.