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By utilizing biorthogonal bases, we develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of the previously overlooked associated state, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues and naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a $1/2$ change of dynamical topological order parameter in biorthogonal bases is observed which is not shown in self-normal bases. Furthermore, we discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state., Comment: 7 pages, 4 figures; Supplemental Material

We apply the static auxiliary field Monte Carlo approach to study phase correlations of the pairing fields in a microscopic model with spin-singlet pairing interaction. We find that the short- and long-range phase correlations are well captured by the phase mutual information, which allows us to construct a theoretical phase diagram containing the uniform $d$-wave superconducting region, the phase fluctuating region, the local pairing region, and the disordered region. We show that the gradual development of phase coherence has a number of consequences on spectroscopic measurements, such as the development of the Fermi arc and the anisotropy in the angle-resolved spectra, scattering rate, entropy, specific heat, and quasiparticle dispersion, in good agreement with experimental observations. For strong coupling, our Monte Carlo simulation reveals an unexpected charge-4$e$ plaquette state with $d$-wave bonds, which competes with the uniform $d$-wave superconductivity and exhibits a U-shaped density of states.

Despite of many efforts, we still lack a clear picture on how heavy electrons emerge and develop on the Kondo lattice. Here we introduce a key concept named the hybridization bond phase and propose a scenario based on phase correlation to address this issue. The bond phase is a gauge-invariant quantity combining two onsite hybridization fields mediated by inter-site magnetic correlations. Its probabilistic distribution decays exponentially with site distance, from which a characteristic length scale can be extracted to describe the spatial correlation of Kondo hybridizations. Our calculations show that this correlation length grows logarithmically with lowering temperature at large Kondo coupling, and reveal a precursor pseudogap state with short-range phase correlation before long-range phase coherence is developed to form the Kondo insulating (or heavy electron) state at low temperatures. This provides a potential microscopic explanation of the two-stage hybridization proposed by recent pump-probe experiment and the logarithmic scaling in the phenomenological two-fluid model. Our work offers a novel theoretical framework to describe the phase-related physics in Kondo lattice systems., Comment: 9 pages, 5 figures

We propose a static auxiliary field approximation to study the hybridization physics of Kondo systems without the sign problem and use the mutual information to measure the intersite hybridization correlations. Our method takes full account of the spatial fluctuations of the hybridization fields at all orders and overcomes the artificial (first-order) phase transition predicted in the mean-field approximation. When applied to the two-impurity Kondo model, it reveals a logarithmically divergent amplitude mutual information near the so-called "Varma-Jones" fixed point and a large phase mutual information manifesting the development of intersite phase coherence in the Kondo regime, with observable influences on physical properties. These highlight the importance of hybridization fluctuations and confirm the mutual information as a useful tool to explore the hybridization physics in Kondo systems., Comment: 7 pages, 4 figures

We derive an effective classical model to describe the Mott transition of the half-filled one-band Hubbard model in the framework of the dynamical mean-field theory with hybridization expansion of the continuous time quantum Monte Carlo. We find a simple two-body interaction of exponential form and reveal a classical correspondence of the Mott transition driven by a logarithmically divergent interaction length. Our work provides an alternative angle to view the Mott physics and suggests a renewed possibility to extend the application of the quantum-to-classical mapping in understanding condensed matter physics, Comment: 6 pages, 6 figures

Motivated by recent photoemission and pump-probe experiments, we report determinant Quantum Monte Carlo simulations of hybridization fluctuations in the half-filled periodic Anderson model. A tentative phase diagram is constructed based solely on hybridization fluctuation spectra and reveals a crossover regime between an unhybridized selective Mott state and a fully hybridized Kondo insulating state. This intermediate phase exhibits nonlocal hybridization fluctuations and consequentially the so-called "band bending" and a direct hybridization gap as observed in angle-resolved photoemission spectroscopy and optical conductivity. This connects the band bending with the nonlocal hybridization fluctuations as proposed in latest ultrafast optical pump-probe experiment. The Kondo insulating state is only established at lower temperatures with the development of sufficiently strong inter-site hybridization correlations. Our work suggests a unified picture for interpreting recent photoemission, pump-probe, and optical observations and provides numerical evidences for the importance of hybridization fluctuations in heavy fermion physics., Comment: 6 pages, 4 figures

We introduce the functional field integral approach to study the statistics of quantum work under nonequilibrium conditions and derive the general formalism for a bilinear Hamiltonian with arbitrary time dependence. The method is then examined in three models. For the transverse Ising chain, it yields the correct quantum critical scaling and dynamical quantum phase transitions for single and double quench protocols, respectively. For the Su-Schrieffer-Heeger (SSH) model, we observe nonuniversal quantum critical scaling with anomalous $1/N$-correction due to its topological nature. Dynamical quantum phase transitions are observed for three different time evolution protocols but their time periodicity only appears in the double quench case. We then extend our method to the Bardeen-Cooper-Schrieffer (BCS) model for superconductivity and discuss the possibility of its application for general correlated models in combination with either the mean-field approximation or exact Monte Carlo simulations on classical (auxiliary) fields or disorders. Our method has the advantage of numerical simplicity, in the cost of explicit state evolution, and provides a promising way for exploring the physics of quantum work under general conditions., Comment: 13 pages, 9 figures

An unusual correlation function is conjectured by M. Campostrini et al. (Phys. Rev. E 91, 042123 (2015)) for the ground state of a transverse Ising chain with geometrical frustration in one of the translationally invariant cases. Later, we demonstrated the correlation function and showed its non-local nature in the thermodynamic limit based on the rigorous evaluation of a Toeplitz determinant (J. Stat. Mech. 113102 (2016)). In this paper, we prove rigorously that all the states that forming the lowest gapless spectrum (including the ground state) in the kink phase exhibit the same asymptotic correlation function. So, in a point of view of cannonical ensemble, the thermal correlation function is inert to temperature within the energy range of the lowest gapless spectrum., Comment: 8 pages, 0 figures

Traditionally, the transverse spin-1/2 XY model is mapped to a fermionic "c-cycle" problem, where the prior periodic boundary condition is applied to the fermionic chain and the additional boundary term has been neglected. However, the "a-cycle" problem (the original problem without any approximation) has not been treated seriously up to now. In this paper, we consider the XY model with ring frustration and diagonalize it without any approximation with the help of parity constraint. Then two peculiar gapless phases have been found., Comment: 6 pages, 1 figures, to appear in Modern Physics Letters B

Traditionally, the transverse Ising model is mapped to the fermionic c-cycle problem, which neglects the boundary effect due to thermodynamic limit. If persisting on a perfect periodic boundary condition, we can get a so-called a-cycle problem that has not been treated seriously so far (Lieb et al., 1961 \textit{Ann. of Phys.} \textbf{16} 407). In this work, we show a little surprising but exact result in this respect. We find the odevity of the number of lattice sites, $N$, in the a-cycle problem plays an unexpected role even in the thermodynamic limit, $N\rightarrow\infty$, due to the boundary constraint. We pay a special attention to the system with $N(\in Odd)\rightarrow\infty$, which is in contrast to the one with $N(\in Even)\rightarrow\infty$, because the former suffers a ring frustration. As a new effect, we find the ring frustration induces a low-energy gapless spectrum above the ground state. By proving a theorem for a new type of Toeplitz determinant, we demonstrate that the ground state in the gapless region exhibits a peculiar longitudinal spin-spin correlation. The entangled nature of the ground state is also disclosed by the evaluation of its entanglement entropy. At low temperatures, new behavior of specific heat is predicted. We also propose an experimental protocol for observing the new phenomenon due to the ring frustration., Comment: 24 pages, 9 figures

New effects in the frustrated transverse Ising ring are predicted. The system is solved based on a mapping of Pauli spin operators to the Jordan-Wigner fermions. We group the low-lying energy levels into bands after imposing appropriate parity constraint, which projects out the redundant degrees of freedom brought about by the Jordan-Wigner fermions. In the region of strong antiferromagnetic coupling, we uncover an unusual gapless phase induced by the ring frustration. We demonstrate that its ground state exhibits a strong longitudinal spin-spin correlation and possesses a considerably large entropy of entanglement. The low-lying energy levels evolve adiabatically in the gapless phase, which facilitates us to work out new behaviors of density of states, low-temperature correlation functions and specific heat. We also propose an experimental protocol for observing this peculiar gapless phase., Comment: 12 pages (5 letter + 7 supplemental material), 5 figures