Transport in the emergent Bose liquid: Bad metal, strange metal, and weak insulator, all in one system

Transport properties in strongly correlated materials, such as bad metals, strange metals, and weak insulators, defy standard Fermi liquid descriptions; this work investigates these puzzling behaviors by computing temperature-dependent optical conductivity of an emergent Bose liquid and finds that it reproduces all the unexplained features of experiments.

The gist

The unification of all these non-Fermi liquid behaviors in a single model suggests that a new quantum state of matter, namely the emergent Bose liquid, will guide the development of the next generation of solid state physics.

Experimental Puzzles Addressed

The paper addresses several atypical transport characteristics observed in strongly correlated materials:

1. Bad metal behavior: non-saturating resistivity at high temperature beyond the Mott-Ioffe-Regel (MIR) limit, which defies standard theories relating it to thermally enabled incoherent scattering of fermionic carriers.

2. Strange metal behavior: a temperature T-linear resistivity at low temperature, which is difficult to understand from the standard picture of fermionic quasi-particles because it contradicts the expectation that resistivity should start at zero at T = 0 and grow with a power higher than linear in Fermi liquid theory.

3. Weak insulating behavior: a crossover to an insulator-like growth of resistivity in the low-temperature limit, which cannot be described by the typical activation energy scale formula like e∆/T.

The Emergent Bose Liquid Model

The core of the proposed solution is replacing fermionic carriers with bosonic ones that emerge at some high energy scale, consistent with shot noise experiments suggesting carriers far from superconductivity have charge 2e. The conditions resulting in an emergent Bose liquid (EBL) begin with a strong intra-atomic repulsion with corresponding short-range correlations at high energy. If a binding mechanism becomes relevant at lower energies, the physics is dominated by bosons formed from nearest neighbor carriers, which have centers at the bonds of the underlying fermion lattice and extended hardcores forbidding occupation of surrounding bounds due to high energy constraints.

Explanation of Optical Conductivity Features

The EBL model provides a clear physical explanation for features observed in optical conductivity:

1. An overwhelming continuum exhausting most of the spectral weight originates from gapless inter-band transitions, which are gapless because all bosons participate due to a lack of a Pauli principle.

2. A mid-infrared feature around 100meV rises out of this continuum due to transitions between the two van-Hove singularities, which are weakly doping dependent. This reveals an scale hidden in the kinetic energy of the underlying fermionic lattice.

3. The lack of a superconducting gap signature around 2∆SC is self-evident in a system of bosons, as the bosonic band structure generates superfluidity without opening a gap, meaning an onset at the 2∆SC gap scale should not occur.

Unification of Transport Behaviors

By taking the DC-limit (ω → 0) above the BEC transition, the EBL model explains all resistivity behaviors:

1. The strange metal behavior results in a linear resistivity over a broad temperature range with a slope that decreases as doping increases, consistent with Eq.(5).

2. The weak insulating behavior occurs at lower temperatures just above the superconducting transition, where Eq.(4) becomes more divergent as temperature is further decreased, which is explained by bosons being confined to low-energy states and losing velocity.

3. The bad metal behavior is inevitable with unbounded resistivity as temperature increases, resulting from the reduction of carrier density at low frequency and is correspondingly accompanied by a weight transfer to a higher frequency regime, a mechanism distinct from scattering-dominated considerations in fermionic systems.

Conclusion and Significance

The EBL paradigm offers an intuitive physical understanding of these exotic transport features without relying on exotic scattering to destroy the particle nature while retaining the fermionic description. The multi-orbital nature of the EBL is crucial, as it provides the necessary flexibility for weight transfer to high energy in optical conductivity, distinguishing it from standard bosonic pictures. This model serves as a universal low-energy paradigm for a large class of strongly correlated materials and guides future solid state physics research. The intra-atomic repulsion scale (∼ 8eV) and short-range antiferromagnetic correlation scale (∼ 150meV) in cuprates are well beyond the relevant energy scales, providing adequate high energy constraints for the EBL assumptions.

Key Mathematical Relationships

The dominant temperature and doping dependence of optical conductivity is given by:

(3)

(4)

Where resistivity is represented via a typical component ρk as:

(4)

Summary of Key Findings and Support

1. The EBL reproduces all the phenomena described above semi-quantitatively, including bad metal, strange metal, weak insulator, and all essential features of optical conductivity.

As a fastidious researcher, I have analyzed this paper, Transport in the emergent Bose liquid: Bad metal, strange metal, and weak insulator, which proposes an Emergent Bose Liquid (EBL) model to unify non-Fermi liquid transport phenomena in strongly correlated materials.

The core insight is replacing fermionic carriers with bosonic ones that emerge at high energy scales and utilizing a multi-orbital nature to explain features observed in both DC resistivity and optical conductivity.

Here are the specific improvements for AI systems based on the principles derived from this physical model:

1. Improved Material Simulation and Modeling

High-fidelity simulation of strongly correlated materials (like cuprates or iron pnictides) currently relies heavily on computationally expensive Density Functional Theory (DFT) or Hubbard models, which often struggle to capture emergent, non-Fermi liquid behavior accurately at low energies.

The EBL framework suggests a more efficient approach: instead of trying to model complex fermionic scattering mechanisms directly, the AI system should be trained to identify and map the emergent bosonic degrees of freedom and their associated high-energy constraints (intra-atomic repulsion, bond structure).

The improved AI system can:

• Perform bosonization transformations on complex fermionic systems (e.g., via neural network approximations of the EBL Hamiltonian) to simplify the simulation space.

• Predict transport properties by calculating the dynamics of these emergent bosons, which should inherently reproduce features like the temperature-linear resistivity (strange metal) and saturation/crossover behaviors (bad metal/weak insulator) without requiring complex, ad-hoc scattering terms.

2. Enhanced Predictive Capability for Non-Equilibrium Transport

The paper successfully links DC transport (resistivity) and optical response to a single underlying bosonic picture. This suggests that the AI should be designed to handle coupled, multi-scale dynamics simultaneously.

The improved AI system can:

• Simulate dynamic responses across vastly different energy scales (from 100 meV mid-infrared features up to eV charge transfer gaps) using the EBL's inherent multi-orbital structure.

• Predict how temperature and doping variations affect the spectral weight transfer mechanism described in Figure 4, allowing for accurate modeling of high-frequency response in functional materials under varying conditions.

3. Automated Identification of Quantum Phases (Phase Diagram Mapping)

The EBL model provides a unified paradigm that explains multiple disparate experimental observations (bad metal, strange metal, weak insulator) within one single quantum state.

The improved AI system can:

• Analyze large datasets from experimental techniques (transport measurements and optical spectroscopy) and automatically classify the underlying quantum phase by testing which emergent bosonic configuration best reproduces the observed features across both DC and AC spectra.

• Identify hidden phases or crossovers that defy standard Fermi liquid classification, potentially discovering new material classes dominated by EBL physics before they are explicitly synthesized.

4. Reduced Computational Complexity via Phenomenological Mapping

The paper notes that the temperature-independent broadening used in the EBL model is sufficient to explain many experimental observations, suggesting a reduction in the need for extremely complex, temperature-dependent scattering rate calculations.

The improved AI system can:

• Utilize simplified, physically intuitive parameters (like high-energy constraints and bond structure) instead of requiring full time-dependent fermionic scattering solvers. This leads to significantly faster inference and simulation times for predicting transport characteristics in novel or unexplored materials.

5. Guiding Experimental Material Design

By understanding the underlying energy scales (e.g., intra-atomic repulsion 8eV, magnetic correlations 150meV) that define the EBL, the AI can guide material synthesis efforts toward optimizing these constraints for desired functional properties.

The improved AI system can:

• Design target material structures (lattice geometries or doping profiles) that maximize the favorable multi-orbital interactions necessary to stabilize the emergent Bose liquid phase.

Non-saturating high-temperature resistivity ("bad metal"), T-linear low-temperature resistivity ("strange metal"), and a crossover to activation-free growth of the resistivity in the low-temperature limit ("weak insulator") are among the most exotic behaviors widely observed in many strongly correlated materials for decades that defy the standard Fermi liquid description of solids. Here we investigate these puzzling behaviors by computing temperature-dependent optical conductivity of an emergent Bose liquid and find that it reproduces all the unexplained features of the experiments, including a featureless continuum and a well-known mid-infrared peak. Amazingly and with physically intuitive mechanisms, the corresponding doping- and temperature-dependent resistivity displays the bad metal and strange metal simultaneously and sometimes weak insulating behaviors as well. The unification of all these non-Fermi liquid behaviors in a single model suggests that a new quantum state of matter, namely the emergent Bose liquid, will guide the development of the next generation of solid state physics.