Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provi
des access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT+DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT+ED simulations.
While the Mott transition from a Fermi liquid is correctly believed to obtain without the breaking of any continuous symmetry, we show that in fact a discrete emergent $mathbb Z_2$ symmetry of the Fermi surface is broken. The extra $mathbb Z_2$ symme
try of the Fermi liquid appears to be little known although it was pointed out by Anderson and Haldane and we use it here to classify all possible Fermi liquids topologically by invoking K-homology. It is this $mathbb Z_2$ symmetry breaking that signals the onset of particle-hole asymmetry, a widely observed phenomenon in strongly correlated systems. In addition from this principle, we are able to classify which interactions suffice to generate the $mathbb Z_2$-symmetry-broken phase. As this is a symmetry breaking in momentum space, the local-in-momentum space interaction of the Hatsugai-Kohmoto (HK) model suffices as well as the Hubbard interaction as it contains the HK interaction. Both lie in the same universality class as can be seen from exact diagonalization. We then use the Bott topological invariant to establish the stability of a Luttinger surface. Our proof demonstrates that the strongly coupled fixed point only corresponds to those Luttinger surfaces with co-dimension $p+1$ with $p$ odd. Because they both lie in the same universality class, we conclude that the Hubard and HK models are controlled by this fixed point.
In the hole-doped cuprates, the pseudogap refers to a suppression of the density of states at low energies, in the absence of superconducting long-range order. Numerous calculations of the Hubbard model show a pseudogap in the single-particle spectra
, with striking similarities to photoemission and tunneling experiments on cuprates. However, no clear mechanism has been established. Here, we solve the Hubbard model on $2times2$ clusters by exact diagonalization, with integration over twisted boundary conditions. A pseudogap is found in the single-particle density of states with the following characteristics: a decreasing energy scale and onset temperature for increased hole-doping, closure at a critical hole doping near 15%, absence upon electron-doping, particle-hole asymmetry indicated by the location of the gap center, and persistence in the strong-coupling limit of $U/t to infty$. Studying the many-body excitation spectrum reveals that the pseudogap in single-particle spectra is due to orthogonality between bare electrons and the lowest energy excitations for $U/t gtrsim 8$.
We employ Momentum-Resolved Electron Energy Loss Spectroscopy (M-EELS) on Bi2.1Sr1.9CaCu2O8+x to resolve the issue of the kink feature in the electron dispersion widely observed in the cuprates. To this end, we utilize the GW approximation to relate
the density response function measured in in M-EELS to the self-energy, isolating contributions from phonons, electrons, and the momentum dependence of the effective interaction to the decay rates. The phononic contributions, present in the M-EELS spectra due to electron-phonon coupling, lead to kink features in the corresponding single-particle spectra at energies between 40 meV and 80 meV, independent of the doping level. We find that a repulsive interaction constant in momentum space is able to yield the kink attributed to phonons in ARPES. Hence, our analysis of the M-EELS spectra points to local repulsive interactions as a factor that enhances the spectroscopic signatures of electron-phonon coupling in cuprates. We conclude that the strength of the kink feature in cuprates is determined by the combined action of electron-phonon coupling and electron-electron interactions.
Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable system that is a prototyp
ical Mott insulator above a critical interaction strength at half filling. Upon doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the BCS state, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies as seen in the cuprates as well as a suppression of the superfluid density relative to that in BCS theory.
While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLE
X+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.
Strange or bad metallic transport, defined by its incompatibility with conventional quasiparticle pictures, is a theme common to strongly correlated materials and ubiquitous in many high temperature superconductors. The Hubbard model represents a min
imal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 the non-interacting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.
The superconducting (SC) and charge-density-wave (CDW) susceptibilities of the two dimensional Holstein model are computed using determinant quantum Monte Carlo (DQMC), and compared with results computed using the Migdal-Eliashberg (ME) approach. We
access temperatures as low as 25 times less than the Fermi energy, $E_F$, which are still above the SC transition. We find that the SC susceptibility at low $T$ agrees quantitatively with the ME theory up to a dimensionless electron-phonon coupling $lambda_0 approx 0.4$ but deviates dramatically for larger $lambda_0$. We find that for large $lambda_0$ and small phonon frequency $omega_0 ll E_F$ CDW ordering is favored and the preferred CDW ordering vector is uncorrelated with any obvious feature of the Fermi surface.
A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emerg
ence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.
We present determinant quantum Monte Carlo simulations of the hole-doped single-band Hubbard-Holstein model on a square lattice, to investigate how quasiparticles emerge when doping a Mott insulator (MI) or a Peierls insulator (PI). The MI regime at
large Hubbard interaction $U$ and small relative electron-phonon coupling strength $lambda$ is quickly suppressed upon doping, by drawing spectral weight from the upper Hubbard band and shifting the lower Hubbard band towards the Fermi level, leading to a metallic state with emergent quasiparticles at the Fermi level. On the other hand, the PI regime at large $lambda$ and small $U$ persists out to relatively high doping levels. We study the evolution of the $d$-wave superconducting susceptibility with doping, and find that it increases with lowering temperature in a regime of intermediate values of $U$ and $lambda$.
