|title||Exact eigenstates and weak ergodicity breaking in multicomponent Hubbard models|
The $\eta$-pairing state is an exact superfluid eigenstate of the Fermi-Hubbard model constructed by C. N. Yang . In this work, we construct exact eigenstates of multicomponent Hubbard models, which include the SU(N) Hubbard model as a special case, by generalizing the $\eta$-pairing mechanism . The generalized $\eta$-pairing eigenstates are formed through simultaneous condensation of multiple types of fermion pairs and shown to exhibit off-diagonal long-range order coexisting with magnetic long-range order. Unlike the two-component case, these exact eigenstates do not arise from symmetry of the Hamiltonian, but originate from a restricted spectrum-generating algebra supported by the Pauli exclusion principle. Building on this fact, we show that the generalized $\eta$-pairing eigenstates do not obey the eigenstate thermalization hypothesis and can be regarded as quantum many-body scar states. This result indicates that the N-component Hubbard models show weak ergodicity breaking for $N \geq 3$.
 C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989).
 M. Nakagawa, H. Katsura, and M. Ueda, in preparation.
|title||Measurement induced phase fixation in discrete space|
|abstract||We find that in a lattice space, the wave function of free particles develop a fixed relation of its complex phases at different sites when general continuous position measurement is present, and as a consequence, the expectation value of the energy becomes constantly zero at each single trajectory level, and the expection value of the energy cannot be perturbed by the stochastic measurement outcome. We discuss the properties and the generality of this result, and we show how this phase relation is developed, and discuss the conditions for developing this phase relation.|
|title||Quantum many-body scar states in a Rydberg-atom chain with hopping|
Recently, unusual initial states have been experimentally discovered which does not reach the thermal equilibrium for an anomalously long time in contrast to the rapid thermalization of the majority of initial states. Motivated by this result, intensive research has been conducted investigating quantum many-body scar states, which exhibit an extremely slow thermalization or even absence of it. In the system discussed in Ref., atoms trapped in an optical lattice are described as two-level systems, in which the high-energy level, called the Rydberg state, exhibits a strong repulsion with neighboring ones.
Here, to gain an insight into the emergence of quantum many-body scar states and thermalization, we investigate the situation in which there are unoccupied sites and atoms can hop between nearest-neighbor sites, while in the original study atoms are fixed at each site. Specifically, we numerically obtain the energy spectrum and eigenstates as well as their entanglement entropy for a small number of sites and atoms. We show the existence of a series of low-entangled states and analyze their property. Furthermore, we discuss their influence on the dynamics and an algebraic relationship among some of them.
(This research is conducted in the self-directed joint-research project as a part of the course work of the leading graduate school MERIT.)
H. Bernien et al., Nature 551, 579 (2017).
|title||Game-Theoretical Models on a Graph|
|abstract||Game theory is commonly used to explain human decision-making processes and has an important role in economics, biology and other various fields. In this seminar, we would see a game-theoretical model with a large population on a graph and Pairwise-Fermi update rule. We mainly focus on what is called the prisoner's dilemma game, where two rational players are likely to mutually defect and fail to reach the optimal choices for both players. In this model, a phase transition behavior can be observed with respect to the coefficient of cost-to-benefit ratio and the strength of natural selection.|
|title||Nonlinear Landauer Formula|
The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear quantum Hall effect. We establish a new connection between the nonlinear quantum Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear quantum Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.
Reference: K. Kawabata and M. Ueda, arXiv:2110.08304
|title||Heating in many-body systems under fast and strong driving|
|abstract||Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. Here, we provide a simple formula on the heating rate under fast and strong periodic driving in classical and quantum many-body systems. The key idea behind the formula is constructing a time-dependent dressed Hamiltonian by moving to a rotating frame, which is found by a truncation of the high-frequency expansion of the micromotion operator, and applying the linear-response theory to the dressed Hamiltonian, rather than the bare Hamiltonian. It is confirmed for specific classical and quantum models that the second-order truncation of the high-frequency expansion yields quantitatively accurate heating rates beyond the linear-response regime. Our result implies that the information on heating dynamics is encoded in the first few terms of the high-frequency expansion, although heating is often associated with an asymptotically divergent behavior of the high-frequency expansion.
Reference: T. Mori, arXiv:2107.12587
|title||Stochastic Neural Networks with Infinite Width are Deterministic|
|abstract||In this work, we show the predictive variance of a trained stochastic neural network tends to zero as its width tends to infinity. Our results shed light on how stochastic neural networks work and have important implications for distribution modeling with neural networks and Bayesian deep learning.|
|title||An attempt to construct a quantum information engine on a tilted 1D periodic potential|
|abstract||Traditionally, people use Maxwell's demon to construct classical information engines by harnessing the thermal fluctuations. Recently, a minimal model of quantum information engine fueled by pure quantum measurements without the aid of a thermal bath has been proposed. It consists of a two-level system and work can be extracted by simply performing measurements on the qubit. We attempt to construct a quantum information engine in a tilted potential using measurement and feedback control. In this seminar, I'm going to review classical and quantum information engines, the Bloch oscillation, and then describe our problem setup.|