Session F43: Precision many-body physics III: Non-perturbative QFT

Particle transmutations in flat-band lattices: bosons to fermions, fermions to composite fermions

Understanding new quantum states and exotic quasiparticles can often be facilitated by approaching the problem in a different basis. One such example, amongst many, is viewing hard core bosons as fermions coupled to a special gauge-field (called the Chern-Simons gauge field). The non-Maxwellian nature of this gauge field introduces new challenges in treating such a problem. However, progress has been made by treating the problem via various mean-field schemes. In this talk, we will draw our attention to the consequences of one particular scheme that is designed to be applicable for various interesting 2D lattices. We will see how this scheme leads to a particular intra-unit cell flux distribution that provides a natural description of the system in the parameter space where a chiral spin-liquid is stabilized for bosons residing in either a Honeycomb lattice or a Kagome lattice. We will view these results in light of other numerical works in the literature. Interestingly, we will also see that when the same scheme is applied to fermions in a lattice, subject to an external magnetic field, we can make interesting predictions related to the composite fermion state: in particular the theory suggests that Graphene with next nearest neighbor hopping at the half-filling condition should be a doped Haldane-Chern insulator of composite fermions.   

Coherent states, Gram matrix, and Hofstadter butterfly with flat band

Through a concrete example, we illustrate that the correspondence between Gram matrices and Hamiltonians may open up grand opportunities to discover novel systems. We find that the Gram matrices of certain subsets of coherent states, whose associating eigenvalues form a lattice on the complex plane, can be interpreted as Hamiltonians which govern the dynamics of a particle hopping around the lattice under a gauge field. The completeness of the subsets of coherent states guarantees massive degeneracy of the ground states of the Hamiltonians, which is independent from the shape of the lattice, while different types of lattice result in different Hofstadter-butterfly-like patterns in the excitation spectrum. The models also feature ground state wave functions in universal form whose dynamics is special. Numerical evidence suggests that it is highly possible to study the models experimentally.   

Chern-Simons fermionization approach to the chiral spin liquid on a frustrated square lattice with moat band

We utilize the Chern-Simons (CS) fermionization to study quantum spin XY models on a square lattice in the regime where the lattice dispersion exhibits a moat-like structure. We analytically derive the low-energy effective field theory, and predict a possible non-uniform chiral spin-liquid (CSL) ground state. Using high-precision numerical calculations such as the tensor network renormalization group based on projected entangled paired state (PEPS), we obtain numerical evidences that further suggest the stabilization of the non-uniform CSL. Finally, we show that the CS fermionization approach is also able to describe the magnetically ordered phases, which are captured by a CS superconducting state with condensation of Cooper pairs of CS fermions. By comparing the Goldstone mode of the magnetically ordered phase and that of the CS superconductor, we found high-precision agreements that suggest the equivalence of the two states in terms of the low-energy excitations.   

Viscous Topological Electromagnetic Phases of Matter

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number for electromagnetic waves coupled to matter $C\neq 0$. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial $C\neq 0$ leading to unidirectional transverse electromagnetic edge waves when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.   

Imaging impurities at quantum Hall edges in graphene: Dissipation rings induced by forward scattering

Motivated by the recent experiment by Marguerite et al. on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. Briefly, the impurity induced forward scattering of quantum Hall particles leads to an enhanced phonon emission, which reaches its maximum when the impurity state is fine tuned to its resonance by an applied tip voltage. Our analysis of the effect of a tip potential on the dissipation thus reveals peculiar thermal rings near the impurity, in consistency with experimental observations. This thermal ring behavior, while appearing similar as that in two dimensional materials, turns out to be physically novel and contains features that are unique in quantum Hall systems.   

Repulsive Casimir force in time-reversal symmetry broken media

In quantum field theory, a vacuum is not empty but full of fluctuating electromagnetic waves. If two dielectric mirrors (silicon plates) are placed facing each other in vacuum, it is well known that there exists an attractive Casimir force between them. When one of the silicon plates is replaced by a medium with time-reversal symmetry breaking (usually achieved by an external magnetic field), we show that the Casimir force can become repulsive. This opens the possibility of controlling the quantum vacuum with non-reciprocal media.   

Supersymmetry approach to interacting disordered systems: the SYK model

In this talk, we propose a new, supersymmetric sigma-model representation for interacting disordered fermion systems. To derive it, we decouple the interaction Hamiltonian using the conventional Hubbard-Stratonovich approach. Then we notice that the Hubbard-Stratonovich field can, in some situations, be gauged out from the denominator. This enables one to supersymmetrize the interacting theory. The new formalism is tested by calculating the fermion Green's function in the SYK model at large times and is argued to be effective for other interacting models with the disorder.   

Spin and charge correlations across the metal-to-insulator crossover in the half-filled 2d Hubbard model

The 2d Hubbard model with nearest-neighbour hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using diagrammatic Monte Carlo in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and non-local fluctuations in both channels are essential.   

Equation of state and entropy of the doped 2d Hubbard Model

We study thermodynamic properties of the doped Hubbard model with nearest-neighbour hopping on the square lattice by Diagrammatic Monte Carlo and obtain results with controlled error bars in the thermodynamic limit. The behaviour of entropy reveals signatures of the insulating regime developing near half-filling at larger interactions: a maximum in the entropy as a function of density appears as the coupling strength is increased, along with an inflection point near half-filling evidencing a metal to insulator crossover. Cold atom simulations of the Hubbard model which prepare the sample adiabatically will find our data useful for thermometry.   

Pseudogap effects in the unitary Fermi gas and in strongly interacting 2D Fermi gases

Understanding of the unitary Fermi gas of infinite scattering length presents a major challenge owing to the presence of strong correlations. In particular, the existence and extent of a pseudogap regime, in which pairing correlations persist above the superfluid critical temperature, has been extensively debated in the literature. We address the pseudogap question using auxiliary-field quantum Monte Carlo methods on the lattice, optimized to enable large lattice calculations of thermodynamic observables. In particular, we calculate a model-independent energy-staggering pairing gap, which avoids an ill-posed numerical analytic continuation. We extrapolate to the continuum limit, thereby removing finite effective range effects. We use similar methods to study pseudogap effects in interacting 2D Fermi gases along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Our results provide a benchmark for experiments and other strong coupling methods.   

Implicit renormalization approach to the problem of Cooper instability

In the vast majority of cases, superconducting transition takes place at exponentially low temperature Tc out of the Fermi liquid regime. We discuss the problem of determining Tc from known system properties at temperatures T >> Tc, and stress that this cannot be done reliably by following the standard protocol of solving for the largest eigenvalue of the original gap-function equation. However, within the implicit renormalization approach, the gap-function equation can be used to formulate an alternative eigenvalue problem, solving which leads to an accurate prediction for both Tc and the gap function immediately below Tc. With the diagrammatic Monte Carlo techniques, this eigenvalue problem can be solved without invoking the matrix inversion or even explicitly calculating the four-point vertex function. [Phys. Rev. B 100, 064513 (2019)]   

Photoinduced superconducting-like properties: η-pairing and charge stiffness in optically driven Mott-Hubbard systems

We theoretically investigate the electron-electron (superconducting) pairing correlations and charge stiffness in the one-dimensional Hubbard model subjected to a pump electric field. By employing unbiased numerical methods, we show that irradiation of the Mott insulating state of the Hubbard model induces strong pair density-wave-like correlations. The pair density-wave correlations induced here are due to η-pairing states, which are preferentially generated by photoexcitation and possess staggered off-diagonal long-range correlations in the excited states of the Hubbard model. We show that the optically induced η-pairing states give rise to the nonzero charge stiffness, in contrast to the Mott insulating state, where the charge stiffness vanishes. We also discuss the system size dependence associated with the η-pairing state and show that the pairing correlations decay very slowly with system size.   

Pairing tendencies in two-orbital Hubbard models with reduced sign problem

How unconventional superconductivity arises from strong repulsive interactions is a central question in the study of high-temperature superconductivity. Here we study two-orbital Hubbard models with orbital-dependent interaction strength by large-scale Determinantal Quantum Monte Carlo (DQMC) simulations. When one orbital is strongly interacting and the other is weakly or non- interacting, the fermion sign problem is significantly reduced. Temperatures more than two orders of magnitude below the Fermi energy are accessible by DQMC. We present results for the superfluid stiffness and pairfield susceptibilities of such models and comment on their relevance to unconventional superconductors, including the recently discovered superconducting nickelates.