A tensor-network variational formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, a multiscale entanglement renormalization ansatz reproduces an anti-de Sitter black hole at finite temperature. Our finding shows rich functionalities of multiscale entanglement renormalization ansatz as efficient graphical representation of AdS/CFT correspondence.

We present a compelling response of a low-dimensional strongly correlated system to an external perturbation. Using the time-dependent Lanczos method we investigate a nonequilibrium evolution of the half-filled one-dimensional extended Hubbard model, driven by a transient laser pulse. When the system is close to the phase boundary, by tuning the laser frequency and strength, a sustainable charge order enhancement is found that is absent in the Mott insulating phase. We analyze the conditions and investigate possible mechanisms of emerging charge order enhancement. Feasible experimental realizations are proposed.

It is a fundamental task in strongly correlated electron systems to examine interdependence among spin, charge, orbital, and lattice degrees of freedom. Recently, the examinations of the interdependence under nonequilibrium conditions become quite urgent issues in various on-going subjects. Ultrafast transient optics is an approach exploring new functionalities of materials and observing properties hidden in equilibrium conditions. The most important subject is photoinduced phase transition of low-dimensional transition metal oxides and organic materials with strong electron correlation.One-dimensional (1D) Mott insulators, Sr 2 CuO 3 and halogen-bridged Ni compounds, show photoinduced insulator-to-metal transition accompanied with its picosecond recovery to the insulating state. 1,2 The time scale of the recovery is three order of magnitude faster than that for semiconductors. 3 The 1D Mott insulators also exhibit gigantic third-order optical nonlinearity, and because of these two properties, they are promising future opto-electronics materials. 4 The complete description of optically excited Mott insulators is thus desired, but key theoretical concepts in nonequilibrium are still under construction.The photocarriers of the 1D Mott insulators are called holon and doublon representing empty and doubly occupied sites, respectively. A holon and a doublon recombine by emitting energy to other elementary excitations. A problem is to clarify a pass way of energy dissipation due to the recombination. Two possible candidates are spin and phonon excitations, since antiferromagnetic (AF) exchange energy and highest phonon frequencies are of the same order (∼0.1 eV). 5 Since high-energy states created by optical excitation may violate the separation of spin and charge degrees of freedom inherent in 1D electron systems, 6 a pass way for energy dissipation through a spin channel can be expected. However, recent numerical studies have shown robustness of the spin-charge separation for nonequilibrium steady states. 7, 8 It is thus necessary to make clear a coupling of spin and charge degrees of freedom under photoirradiation. As for phonon relaxation, pump-probe experiments have been done for various TTF-TCNQ salts with different magnitudes of electron-phonon (EP) coupling. 9 K-and Rb-TCNQ show spin-Peierls (SP) transition at T c =395 K and 220 K, respectively, and their photocarriers are once localized as polarons at around 70 fs, and then recombine with a few ps. On the other hand, ET-F 2 TCNQ does not show SP transition, and metallic photocarriers decay within 200 fs. Therefore, a fundamental question to be answered is about what is driving force of ultrafast relaxation of the 1D Mott insulators when the charge carriers couple weakly with spin and lattice. Since EP coupling is also present in semiconductors, we need to answer another question why phonon relaxation in the Mott insulators is much faster than that in the semiconductors.In this Letter, we incorporate time dependent vector potential of laser pulse into density-m...

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of "holographic" entanglement entropy. At T(c), the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Furthermore, the spectrum, which is a set of logarithms of the singular values, also seems to be a holographic entanglement spectrum. We find multiple gaps in the spectrum, and in contrast to the topological phases, the low-lying levels below the gap represent spontaneous symmetry breaking. These contrasts are strong evidence of the dual nature of the holography. Based on these observations, we discuss the amount of information contained in one snapshot.

We examine the single-particle excitation spectrum in the one-dimensional Hubbard-Holstein model at half-filling by performing the dynamical density matrix renormalization group (DDMRG) calculation. The DDMRG results are interpreted as superposition of spectra for a spinless carrier dressed with phonons. The superposition is a consequence of robustness of the spin-charge separation against electron-phonon coupling. The separation is in contrast to the coupling between phonon and spin degrees of freedom in two-dimensional systems. We discuss implication of the results of the recent angle-resolved photoemission spectroscopy measurements on SrCuO2.PACS numbers: 71.10. Fd, 74.72.Jt The interplay between electron correlation and electron-phonon coupling is one of the hot topics in the field of strongly correlated electron systems such as high-T c cuprates. Particularly in an electron-removal process from the Mott insulators, the electron-phonon coupling occurs due to charge imbalance around a created hole. Thus, the angle-resolved photoemission spectroscopy (ARPES) is a direct tool, and observes a quasiparticle dressed with phonons [1]. For the twodimensional (2D) insulating cuprates, the ARPES experiments have revealed a broad low-energy peak that is interpleted as a result of disappearance of the quasiparticle weight due to the coupling [2,3,4].The quasiparticle in the 2D systems is not only dressed with phonon cloud, but also dressed with antiferromagnetic (AF) spin fluctuation. Thus, the effect of phonon on the spectrum is affected by the spin configuration of the background. However, in one-dimensional (1D) correlated electron systems, a photohole created by ARPES decays into spinon and holon due to the spin-charge separation [5]. Therefore, the effect of phonon on the spectrum strongly depends on whether the spin-charge separation is robust against the electron-phonon coupling. In this Letter, we examine the effect of phonon on the singleparticle excitation spectrum in 1D Mott insulators.Theoretically, the Hubbard-Holstein model is a basic model to study the interplay between electron correlation and electron-phonon coupling in cuprates [6,7]. However, we have only limited information on the singleparticle excitation spectrum in this model [4,8,9,10,11,12,13]. This is because it is hard to treat the infinite phononic degrees of freedom and electron correlation on an equal footing. In order to overcome the difficulty, we apply the dynamical density matrix renormalization group (DDMRG) method to the calculation of the spec- * Present adress:Department of Physics, Tohoku University, Sendai 980-8578, Japan; Electronic address: matsueda@cmpt.phys.tohoku.ac.jp tra in the half-filled systems.We find the following four characteristic features in the single-particle excitation spectrum: (i) a dip at highbinding energy side of the spinon branch, (ii) broad holon branch, (iii) decrease of the spectral weight of the spinon branch, and (iv) slight enhancement of the weight at lowbinding energy side of the spinon branch. ...