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While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to the experimental probes (transport, quantum capacitance and spectroscopy) of the quantum moir\'e materials such as twisted bilayer graphene and transition metal dichalcogenides. Here we show, by means of momentum-space quantum Monte Carlo and exact diagonalization, there exists a unique thermodynamic characteristic for the correlated flat-band models with interaction-driven quantum anomalous Hall (QAH) ground state, namely, the transition from the QAH insulator to the metallic state takes place at a much lower temperature compared with the zero-temperature single-particle gap generated by the long-range Coulomb interaction. Such low transition temperature comes from the proliferation of excitonic particle-hole excitations, which "quantum teleport" the electrons across the gap between different topological bands to restore the broken time-reversal symmetry and give rise to a pronounced enhancement in the charge compressibility. Future experiments, to verify such generic thermodynamic characteristics, are proposed., Comment: 5 pages, 3 figures with supplemental material

Topological Mott insulator (TMI) with spontaneous time-reversal symmetry breaking and nonzero Chern number has been discovered in a real-space effective model for twisted bilayer graphene (TBG) at 3/4 filling in the strong coupling limit. However, the finite temperature properties of such a TMI state remain illusive. In this work, employing the state-of-the-art thermal tensor network and the perturbative field-theoretical approaches, we obtain the finite-$T$ phase diagram and the dynamical properties of the TBG model. The phase diagram includes the quantum anomalous Hall and charge density wave phases at low $T$, and a Ising transition separating them from the high-$T$ symmetric phases. Due to the proliferation of excitons -- particle-hole bound states -- the transitions take place at a significantly reduced temperature than the mean-field estimation. The exciton phase is accompanied with distinctive experimental signatures in such as charge compressibilities and optical conductivities close to the transition. Our work explains the smearing of the many-electron state topology by proliferating excitons and opens the avenue for controlled many-body investigations on finite-temperature states in the TBG and other quantum moir\'e systems., Comment: 5+15 pages, 4+12 figures

We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum Monte Carlo simulations and an $\epsilon$-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Hence both experimental and numerical investigations will not be representative of the infrared fixed point, but of a crossover regime characterized by drifting exponents., Comment: 35 pages, including a 29 page supplemental information section; added notion of quasiuniversality; updated acknowledgements

We develop a nonequilibrium increment method to compute the R\'enyi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although we still observe similar scaling behavior but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with positivity condition of the R\'enyi entanglement entropy, which holds for unitary conformal field theories(CFT). Our results unambiguously reveal fundamental differences between DQC and quantum critical points(QCPs) described by unitary CFTs., Comment: published version

We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model. The amplitude mode is observed to emerge in the longitudinal spin susceptibility in the presence of a weak symmetry-breaking staggered field. A conventional measure of the amplitude mode in higher dimensions, the singlet bond mode, is found to appear at a lower than the amplitude mode frequency. We identify these two excitations with the second (first) breather of the sine-Gordon theory, correspondingly. In contrast to higher-dimensional systems, the amplitude and bond order fluctuations are found to carry significant spectral weight in the quasi-1D limit., Comment: 16 pages and 8 figures

We report heat capacity measurements of ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ under high pressure along with simulations of relevant quantum spin models and map out the $(P,T)$ phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below $T=2\text{ }\text{ }\mathrm{K}$. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.

We report heat capacity measurements of SrCu_{2}(BO_{3})_{2} under high pressure along with simulations of relevant quantum spin models and map out the (P,T) phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below T=2 K. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune SrCu_{2}(BO_{3})_{2} between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.

Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.

Noether's theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether's theorem at the deconfined quantum critical point (DQCP), which is a quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitation, which could potentially guide the ongoing experimental search for the DQCP in quantum magnets.

The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition, and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling., 4+3 pages, 4+2 figures

An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semimetal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to the 3D $N=4$ Gross-Neveu chiral $XY$ universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.

The nontrivialness of quantum spin liquid (QSL) typically manifests in the non-local observables that signifies their existence, however, this fact actually casts shadow on detecting QSL with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating dynamical signature of anyonic excitations and symmetry fractionalization in QSL. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that across the phase transitions from Z2 QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular the translational symmetry fractionalization of the latter, which can be served as the unique dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) X-ray scatterings., 8 pages,6 figures

Employing large-scale quantum Monte Carlo simulations, we study the extended $XXZ$ model on the kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid and ferromagnet. This $\mathbb{Z}_2$ spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D $XY^*$ universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons., Comment: 7 pages, 8 figures

High-temperature superconductivity is closely adjacent to a long-range antiferromagnet, which is called a parent compound. In cuprates, all parent compounds are alike and carrier doping leads to superconductivity, so a unified phase diagram can be drawn. However, the properties of parent compounds for iron-based superconductors show significant diversity and both carrier and isovalent dopings can cause superconductivity, which casts doubt on the idea that there exists a unified phase diagram for them. Here we show that the ordered moments in a variety of iron pnictides are inversely proportional to the effective Curie constants of their nematic susceptibility. This unexpected scaling behavior suggests that the magnetic ground states of iron pnictides can be achieved by tuning the strength of nematic fluctuations. Therefore, a unified phase diagram can be established where superconductivity emerges from a hypothetical parent compound with a large ordered moment but weak nematic fluctuations, which suggests that iron-based superconductors are strongly correlated electron systems., Comment: 5 pages, 2 figures

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

The amplitude ("Higgs") mode is a ubiquitous collective excitation related to spontaneous breaking of a continuous symmetry. We combine quantum Monte Carlo (QMC) simulations with stochastic analytic continuation to investigate the dynamics of the amplitude mode in a three-dimensional dimerized quantum spin system. We characterize this mode by calculating the spin and dimer spectral functions on both sides of the quantum critical point, finding that both the energies and the intrinsic widths of the excitations satisfy field-theoretical scaling predictions. While the line width of the spin response is close to that observed in neutron scattering experiments on TlCuCl_{3}, the dimer response is significantly broader. Our results demonstrate that highly nontrivial dynamical properties are accessible by modern QMC and analytic continuation methods.

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

We explore possible superconducting states in ${t}_{2g}$ multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, $d$-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund's coupling, which is triggered by antiferromagnetic fluctuations. When the Hund's coupling is comparable to SOC, a twofold degenerate, triplet $p$-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ are discussed.

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.

Using a combination of quantum Monte Carlo simulations, functional renormalization group calculations and mean-field theory, we study the Hubbard model on the Bernal-stacked honeycomb bilayer at half-filling as a model system for bilayer graphene. The free bands consisting of two Fermi points with quadratic dispersions lead to a finite density of states at the Fermi level, which triggers an antiferromagnetic instability that spontaneously breaks sublattice and spin rotational symmetry once local Coulomb repulsions are introduced. Our results reveal an inhomogeneous participation of the spin moments in the ordered ground state, with enhanced moments at the three-fold coordinated sites. Furthermore, we find the antiferromagnetic ground state to be robust with respect to enhanced interlayer couplings and extended Coulomb interactions., 4+ pages, 4 figures; final version