Yuya O. Nakagawa
University of Tokyo
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Featured researches published by Yuya O. Nakagawa.
Nature Communications | 2018
Yuya O. Nakagawa; Masataka Watanabe; Hiroyuki Fujita; Sho Sugiura
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases.The entanglement in a quantum system between a small region and the surrounding environment contains details about the whole state. Nakagawa et al. find a formula for the entanglement entropy of a class of thermal-like states and show that it can be applied more broadly to identify equilibrating states.
Physical Review B | 2018
Ryohei Kobayashi; Masaki Oshikawa; Yuya O. Nakagawa; Yoshiki Fukusumi
Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Restas polarization amplitude (expectation value) in the
Physical Review B | 2016
Yuya O. Nakagawa; Grégoire Misguich; Masaki Oshikawa
S=1/2
Journal of High Energy Physics | 2018
Yuya O. Nakagawa; Gábor Sárosi; Tomonori Ugajin
XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.
Physical Review B | 2017
Yuya O. Nakagawa; Shunsuke Furukawa
We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in presence of a lattice and interactions and we investigate numerically its time-evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains non-vanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.
Physical Review A | 2016
Hiroyuki Fujita; Yuya O. Nakagawa; Yuto Ashida; Shunsuke Furukawa
A bstractOne characteristic feature of a chaotic system is the quick delocalization of quantum information (fast scrambling). One therefore expects that in such a system a state quickly becomes locally indistinguishable from its perturbations. In this paper we study the time dependence of the relative entropy between the reduced density matrices of the thermofield double state and its perturbations in two dimensional conformal field theories. We show that in a CFT with a gravity dual, this relative entropy exponentially decays until the scrambling time. This decay is not uniform. We argue that the early time exponent is universal while the late time exponent is sensitive to the butterfly effect. This large c answer breaks down at the scrambling time, therefore we also study the relative entropy in a class of spin chain models numerically. We find a similar universal exponential decay at early times, while at later times we observe that the relative entropy has large revivals in integrable models, whereas there are no revivals in non-integrable models.
Physical Review B | 2018
Hiroyuki Fujita; Yuya O. Nakagawa; Sho Sugiura; Masaki Oshikawa
We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM). The COE is defined as the fictitious heat capacity calculated from the entanglement spectrum. Its dependence on the fictitious temperature can reflect the low-temperature behavior of the physical heat capacity, and thus provide a useful probe of gapless bulk or edge excitations of the system. Assuming a power-law scaling of the COE with an exponent
arXiv: Statistical Mechanics | 2017
Hiroyuki Fujita; Yuya O. Nakagawa; Sho Sugiura; Masataka Watanabe
\alpha
Journal of Statistical Mechanics: Theory and Experiment | 2017
Yuya O. Nakagawa; Tomonori Ugajin
at low fictitious temperatures, we derive an analytical formula for the distribution function of the RDM eigenvalues. We numerically test the effectiveness of the formula in relativistic free scalar boson in two spatial dimensions, and find that the distribution function can detect the expected
arXiv: Statistical Mechanics | 2018
Hiroyuki Fujita; Masataka Watanabe; Yuya O. Nakagawa; Sho Sugiura
\alpha=3