arXiv subjects

Ying-Jer Kao

Publications and source records attributed to Ying-Jer Kao.

At least 55 records · Page 3Linked to original sources

arXiv2018

Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J \simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.

cond-mat.str-el↗

arXiv2018

Tunneling-induced restoration of classical degeneracy in quantum kagome ice

Quantum effect is expected to dictate the behaviour of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy (TEE) and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a $Z_2$ topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasi-degeneracy of states and effectively, the classical degeneracy is restored.

cond-mat.str-el↗

arXiv2018

Investigation of the 1+1 dimensional Thirring model using the method of matrix product states

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.

hep-lat↗

arXiv2018

Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions.

cond-mat.str-el↗

arXiv2017

Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-$E_x$, Large-$E_y$, or Large-$D$ phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-$D$ critical point is obtained with an unprecedentedly precision, $(D/J)_c=0.9684713(1)$. Close to this critical point, a small rhombic single-ion anisotropy $|E|/J\ll1$ can destroy the Haldane phase and bring the system into a $y$-Néel phase. We propose that the compound [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ is a candidate system to search for the $y$-Néel phase.

cond-mat.str-el↗

arXiv2017

Dynamic scaling in the 2D Ising spin glass with Gaussian couplings

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $τ$ to the system length $L$; $τ\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form.

cond-mat.stat-mech↗

arXiv2017

Tensor Network study of the (1+1)-dimensional Thirring Model

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. We also show the possibility of studying soliton dynamics and topological phase transition via the Thirring model.

hep-lat↗

arXiv2017

Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions.

quant-ph↗

arXiv2017

Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study

The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent $z>1$, which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing $z<1$, when the dynamics of the rare regions is hampered by the longitudinal field.

cond-mat.dis-nn↗

arXiv2016

Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution

Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.

cond-mat.str-el↗

arXiv2016

Field-Induced Ordering in Dipolar Spin Ice

We present numerical studies of dipolar spin ice in the presence of a magnetic field slightly tilted away from the [111] axis. We find a first-order transition from a kagome ice to a $\mathbf{q}=$X state when the external field is tilted toward the $[11\bar{2}]$ direction. This is consistent with the anomalous critical scattering previously observed in the neutron scattering experiment on the spin ice material $\textrm{Ho}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$ in a tilted field [Nat. Phys. 3, 566 (2007)]. We show that this ordering originates from the antiferromagnetic alignment of spin chains on the kagome planes. The residual entropy of the kagome ice is fully recovered. Our result captures the features observed in the experiments and points to the importance of the dipolar interaction in determining ordered states in the spin ice materials. We place our results in the context of recent susceptibility measurements on $\textrm{Dy}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$, showing two features for a [111] field.

cond-mat.stat-mech↗

arXiv2015

Variational Monte Carlo simulations using tensor-product projected states

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.

cond-mat.str-el↗

arXiv2014

Inverse Melting of an Electronic Liquid Crystal

Inverse melting refers to the rare thermodynamic phenomenon in which a solid melts into a liquid upon cooling, a transition that can occur only when the ordered (solid) phase has more entropy than the disordered (liquid) phase, and that has so far only been observed in a handful of systems. Here we report the first experimental observation for the inverse melting of an electronic liquid crystalline order in strontium-doped lanthanum nickelate, a compound isostructural with the superconducting cuprates, with a hole doping concentration of 1/3. Using x-ray scattering, we demonstrate that the isotropic charge modulation is driven to nematic order by fluctuating spins and shows an inverse melting transition. Using a phenomenological Landau theory, we show that this inverse melting transition is due to the interlayer coupling between the charge and spin orders. This discovery points to the importance of the interlayer correlations in the system, and provides a new perspective to study the intricate nature of the electronic liquid crystal phases in strongly correlated electronic systems, including possibly the Cu- and Fe-based high-Tc superconductors.

cond-mat.str-el↗

arXiv2014

Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.

cond-mat.str-el↗

arXiv2014

Long-time dynamics of quantum chains: transfer-matrix renormalization group and entanglement of the maximal eigenvector

By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recent proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012)].

cond-mat.str-el↗

arXiv2013

Half-Magnetization Plateau of a Dipolar Spin Ice in a [100] Field

We report here numerical results of the low-temperature behavior of a dipolar spin ice in a magnetic field along the [100] direction. Tuning the magnetic field, the system exhibit a half-magnetization plateau at low temperature. This half-polarized phase should correspond to a quantum solid phase in an effective 2D quantum boson model, and the transition from the Coulomb phase with a power-law correlation to this state can be regarded as a superfluid to a quantum solid transition. We discuss possible experimental signatures of this half-polarized state.

cond-mat.str-el↗

arXiv2013

Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition

We test an improved finite-size scaling method for reliably extracting the critical temperature $T_{\rm BKT}$ of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness $ρ_s$ at $T_{\rm BKT}$ in combination with the Kosterlitz-Nelson relation between the transition temperature and the stiffness, $ρ_s(T_{\rm BKT})=2T_{\rm BKT}/π$, we define a size dependent transition temperature $T_{\rm BKT}(L_1,L_2)$ based on a pair of system sizes $L_1,L_2$, e.g., $L_2=2L_1$. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining $T_{\rm BKT}(L_1,L_2)$. For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for $L$ up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result $T_{\rm BKT}=0.8935(1)$ is several error bars above the previously best estimates of the transition temperature; $T_{\rm BKT} \approx 0.8929$. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated $T_{\rm BKT}$ because of neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions.

cond-mat.stat-mech↗

arXiv2013

Detection of symmetry-protected topological phases in one dimension with multiscale entanglement renormalization

Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg chain with a single-ion anisotropy D, which has a quantum phase transition between a Haldane phase and a large-D phase. Using symmetric multiscale entanglement renormalization ansatz (MERA) tensor networks, we study the nonlocal order parameters for time-reversal and inversion symmetry. For the inversion symmetric MERA, we propose a brick-and-rope representation that gives a geometrical interpretation of inversion symmetric tensors. Finally, we study the symmetric renormalization group (RG) flow of the inversion symmetric string-order parameter, and show that entanglement renormalization with symmetric tensors produces proper behavior of the RG fixed-points.

cond-mat.str-el↗