arXiv subjects

Kouichi Okunishi

Publications and source records attributed to Kouichi Okunishi.

At least 37 records · Page 2Linked to original sources

arXiv2020

Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions

Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches is the tensor-network strong-disorder renormalization group (tSDRG), which was basically established for one-dimensional (1D) systems. In this paper, we propose a possible improvement of its algorithm toward 2D random spin systems, focusing on a generating process of the tree network structure of tensors, and precisely examine their performances for the random antiferromagnetic Heisenberg model not only on the 1D chain but also on the square- and triangular-lattices. On the basis of comparison with the exact numerical results up to 36 site systems, we demonstrate that accuracy of the optimal tSDRG algorithm is significantly improved even for the 2D systems in the strong-randomness regime.

cond-mat.str-el↗

arXiv2020

Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the $c=1$ boundary conformal field theory associated with the effective $Z_6$ dual sine-Gordon model.

cond-mat.stat-mech↗

arXiv2019

Lattice Unruh effect and world-line entanglement for the XXZ chain

For the XXZ chain, we discuss the relation between a lattice version of Unruh effect and the ground-state entanglement on the basis of the corner Hamiltonian. We find that the lattice Unruh temperature is interpreted as $β_λ= 2π/a$ with an effective acceleration $a=π/λ$, where $λ$ denotes the anisotropy parameter of the XXZ chain. Using quantum Monte Carlo simulation for the corner Hamiltonian at $β_λ$, we demonstrate that world lines of spins surrounding the entangle point provides an intuitive understanding the quantum entanglement. We also propose an XXZ-chain analogue of the detector for the thermalized entanglement spectrum with use of the angular time evolution defined by the corner Hamiltonian.

cond-mat.quant-gas↗

arXiv2018

Snapshot spectra in the world-line quantum Monte Carlo for one-dimensional quantum spin systems

We introduce a snapshot density matrix and snapshot spectrum for world-line (WL) quantum Monte Carlo simulations, by integrating out the continuous-imaginary-time index of WL snapshots. For the transverse-field Ising chain, we reveal fundamental properties of the snapshot spectrum as follows. (i) In the ordered phase, the isolated peak corresponding to the maximum eigenvalue appears, indicating the classical nature of WL configurations. (ii) In the disordered phase, the spectrum converges to the dome-like distribution characterized by an effective aspect ratio of the snapshots. (iii) At the critical point, the power-law distribution is observed with an appropriate scaling analysis of the fixed aspect ratio. For the XXZ chain, we also obtain numerical results consistent with the above properties. In addition, the representation-basis dependence of the snapshot spectrum is also discussed.

cond-mat.stat-mech↗

arXiv2018

Magnetism and high-magnetic field magnetization in alkali superoxide CsO2

Alkali superoxide CsO2 is one of candidates for the spin-1/2 one-dimensional (1D) antiferromagnet, which may be sequentially caused by an ordering of the pi-orbital of O2- molecule below TS ~ 70 K. Here, we report on the magnetism in powder CsO2 and high-magnetic field magnetization measurements in pulsed-magnetic fields of up to 60 T. We obtained the low temperature phase diagram around the antiferromagnetic ordering temperature TN = 9.6 K under the magnetic field. At 1.3 K, remarkable up-turn curvature in the magnetization around a saturation field of ~ 60 T is found, which corresponds to the spin-1/2. We will compare it with the theoretical calculation.

cond-mat.mtrl-sci↗

arXiv2017

Critical behavior of the two-dimensional icosahedron model

In the context of a discrete analogue of the classical Heisenberg model, we investigate critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to vertices of the icosahedron. Effective correlation length and magnetization of the model are calculated by means of the corner-transfer matrix renormalization group (CTMRG) method. Scaling analysis with respect to the cutoff dimension $m$ in CTMRG reveals the second-order phase transition characterized by the exponents $ν= 1.62\pm0.02$ and $β= 0.12\pm0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the minimal series of conformal field theory.

cond-mat.stat-mech↗

arXiv2017

Phase Transitions for Cuboc Orders in Stacked Kagome Heisenberg Systems

Using the event-chain Monte Carlo (MC) algorithm, we investigate phase transitions of the stacked Kagome Heisenberg systems with classical vector spins including up to the 3rd-nearest-neighbor couplings. In particular, we focus on two types of non-coplanar spin orders ---cuboc1 and cuboc2 orders, both of which have twelve-sublattice structures accompanying the translational-symmetry breaking. We perform event-chain MC simulations up to L=72, where L represents the linear dimension of the stacked Kagome lattice, and then find that the cuboc1 transition shows 2nd-order-transition behaviors with a tendency to a weak-1st-order transition up to L=72, while the cuboc2 transition is basically described by the 1st-order transition. We then discuss the above transitions in connection with the effective Landau-Ginzburg-Wilson theory with the O(3)xO(3) symmetry.

cond-mat.stat-mech↗

arXiv2017

Spin-wave analysis for Kagome-triangular spin system and coupled spin tubes: low-energy excitation for the cuboc order

The coupled spin tube system, which is equivalent to a stacked Kagome-triangular spin system, exhibits the cuboc order -- a non-coplanar spin order with a twelve-sublattice structure accompanying spontaneous breaking of the translational symmetry -- in the Kagome-triangular plane. On the basis of the spin-wave theory, we analyze spin-wave excitations of the planar Kagome-triangular spin system, where the geometric phase characteristic to the cuboc spin structure emerges. We further investigate spin-wave excitations and dynamical spin structure factors for the coupled spin tubes, assuming the staggered cuboc order.

cond-mat.str-el↗

arXiv2016

Sine-square deformation and Mobius quantization of two-dimensional conformal field theory

Motivated by sine-square deformation (SSD) for quantum critical systems in 1+1-dimension, we discuss a Mobius quantization approach to the two-dimensional conformal field theory (CFT), which bridges the conventional radial quantization and the dipolar quantization recently proposed by Ishibashi and Tada. We then find that the continuous Virasoro algebra of the dipolar quantization can be interpreted as a continuum limit of the Virasoro algebra for scaled generators in the SSD limit of the Mobius quantization approach.

hep-th↗

arXiv2015

Sine-square deformation and supersymmetric quantum mechanics

We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions. We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD.

cond-mat.stat-mech↗

arXiv2015

Magnetic phase diagram of the coupled triangular spin tubes for CsCrF4

Using Monte Carlo simulations, we explore the magnetic phase diagram of the triangular spin tubes coupled with a ferromagnetic inter-tube interaction for CsCrF4. A planar structure of the coupled tubes is topologically equivalent to the Kagome-triangular lattice, which induces nontrivial frustration effects in the system. We particularly find that, depending on the inter-tube coupling, various ordered phases are actually realized, such as incommensurate order, ferromagnetic order, and Cuboc order, which is characterized by the non-coplanar spin structure of the twelve sublattice accompanying the spin chirality breaking. We also discuss a relevance of the results to recent experiments of CsCrF4.

cond-mat.stat-mech↗

arXiv2014

Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems

We investigate the eigenvalue distribution of the snapshot density matrix (SDM) generated by Monte Carlo simulation for two-dimensional classical spin systems. We find that the distribution in the high-temperature limit is well explained by the random-matrix theory, while that in the low-temperature limit can be characterized by the zero-eigenvalue condensation. At the critical point, we obtain the power-law distribution with a nontrivial exponent $α\equiv(2-η)/(1-η)$ and the asymptotic form of the snapshot entropy, on the basis of the relationship of the SDM with the correlation function matrix. The aspect-ratio dependence of the SDM spectrum is also mentioned.

cond-mat.stat-mech↗

arXiv2014

Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains

Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, the Kennedy-Tasaki transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present the temperature dependence of the energy, entropy and string order parameter for the SO(N=3, 4, 5) BLBQ chains by a world-line Monte-Carlo simulation for the N-color bosonic particle model.

cond-mat.stat-mech↗

arXiv2014

Fine-Tuning of Magnetic Interactions in Organic Spin Ladders

We have succeeded in synthesizing two types of new organic radical crystals 3-I-V [= 3- (3-iodophenyl)-1,5-diphenylverdazyl] and 3-Br-4-F-V [= 3-(3-bromo-4-fluorophenyl)-1,5- diphenylverdazyl]. Their crystal strucutures are found to be isomorphous to that of previously reported spin ladder 3-Cl-4-F-V. Through the quantitative analysis of their molecular arrangements and magnetic properties, we confirm that these materials form ferromagnetic chain-based spin ladders with slightly modulated magnetic interactions. These results present the first quantitative demonstration of the fine-tuning of magnetic interactions in the molecular- based materials.

cond-mat.str-el↗

arXiv2014

Doubling of Entanglement Spectrum in Tensor Renormalization Group

We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by `doubling' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D = 64$, where $D$ is the cut-off dimension of tensors. At the critical point, we also find that a non-trivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

cond-mat.stat-mech↗

arXiv2012

Wilson's numerical renormalization group and AdS_3 geometry

We discuss the relation between the Wilson's numerical renormalization group(NRG) for the Kondo impurity problem and a field theory in the background AdS_3 space time, where the radial coordinate plays a role of the controlling parameter of the effective mass scale. We find that the Wilson NRG can be described by the boundary Rindler field and then the cutoff parameter λof the Wilson NRG is related to the AdS radius L through λ= 2k_F/ωL, where k_F is the effective Fermi wave number. It is also found that the Rindler space is discretized with the lattice space of a=π/k_F.

hep-th↗

arXiv2012

Spin-Chirality Separation and S_3-Symmetry Breakings in the Magnetization Plateau of the Quantum Spin Tube

We study the magnetization plateau state of the three-leg spin-1/2 tube in the strong rung coupling region, where S_3-symmetry breakings and low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless non-magnetic excitations, the spin imbalance phase and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.

cond-mat.str-el↗

arXiv2010

Topological disentangler for the valence-bond-solid chain

We discuss topological disentangler for S=1 quantum spin chains in the Haldane phase. We first point out that Kennedy-Tasaki's(KT) nonlocal unitary transformation is the perfect disentangler for Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the double-fold degeneracy in the entanglement spectrum of the S=1 Heisenberg chain.

cond-mat.stat-mech↗