arXiv subjects

Ning-Hua Tong

Publications and source records attributed to Ning-Hua Tong.

At least 37 records · Page 2Linked to original sources

arXiv2018

Impurity-Induced Environmental Quantum Phase Transitions in the Quadratic-Coupling Spin-Boson Model

We study the zero temperature properties of the sub-Ohmic spin-boson model with quadratic spin-boson coupling. This model describes experimental set ups at the optimal working point where the linear-coupling between the qubit (spin) and the environmental noise (bosons) is zero and the leading coupling is quadratic. In the strong coupling regime, we find that the existence of spin induces quantum phase transitions (QPTs) between two states of environment: the normal state and a state with local distortions. The phase diagram contains both continuous and the first-order QPTs, with non-trivial critical properties obtained exactly. At the QPTs, the equilibrium state spin dynamics bears power-law $ω$ dependence in the small frequency limit and a robust coherent Rabi oscillation at high frequency. We discuss the feasibility of observing such environmental QPTs in the qubit-related experiments.

cond-mat.mes-hall↗

arXiv2017

Dynamical Correlation Functions of the Quadratic Coupling Spin-Boson Model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions $C_{O}(ω)$, with the operator $\hat{O}$ taken as $\hatσ_x$, $\hatσ_z$, and $\hat{X}$, respectively. In the weak-coupling regime $α< α_c$, these functions show power law $ω$-dependence in the small frequency limit, with the powers $1+2s$, $1+2s$, and $s$, respectively. At the critical point $α= α_c$ of the boson-unstable quantum phase transition, the critical exponents $y_{O}$ of these correlation functions are obtained as $y_{σ_x} = y_{σ_z} = 1-2s$ and $y_{X}=-s$, respectively. Here $s$ is the bath index and $X$ is the boson displacement operator. Close to the spin flip point, the high frequency peak of $C_{σ_{x}}(ω)$ is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

cond-mat.mes-hall↗

arXiv2017

Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model Under Bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function $C(ω)$ of the spin operator $σ_z$ for the biased sub-Ohmic spin-boson model. The small-$ω$ behavior $C(ω) \propto ω^s$ is found to be universal and independent of the bias $ε$ and the coupling strength $α$ (except at the quantum critical point $α=α_c$ and $ε=0$). Our NRG data also show $C(ω) \propto χ^{2}ω^{s}$ for a wide range of parameters, including the biased strong coupling regime ($ε\neq 0$ and $α> α_c$), supporting the general validity of the Shiba relation. Close to the quantum critical point $α_c$, the dependence of $C(ω)$ on $α$ and $ε$ is understood in terms of the competition between $ε$ and the crossover energy scale $ω_{0}^{\ast}$ of the unbiased case. $C(ω)$ is stable with respect to $ε$ for $ε\ll ε^{\ast}$. For $ε\gg ε^{\ast}$, it is suppressed by $ε$ in the low frequency regime. We establish that $ε^{\ast} \propto (ω_0^{\ast})^{1/θ}$ holds for all sub-Ohmic regime $0 \leqslant s < 1$, with $θ=2/(3s)$ for $0 < s \leqslant 1/2$ and $θ= 2/(1+s)$ for $1/2 < s < 1$. The variation of $C(ω)$ with $α$ and $ε$ is summarized into a crossover phase diagram on the $α-ε$ plane.

cond-mat.mes-hall↗

arXiv2015

Equation of Motion Series Expansion of Double Time Green's Functions

Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double time Green's function into Taylor series of the parameter $λ$ in the Hamiltonian $H=H_0 + λH_1$. Here $H_0$ is the exactly solvable part and $H_1$ is regarded as the perturbation. To restore the analytical structure of GF, we use the continued fraction to do resummation for the obtained series. The problem of zero-temperature divergence is identified and remedied by the self-consistent series expansion. To demonstrate the implementation of this method, we carry out the weak- as well as the strong-coupling expansion for the Anderson impurity model to order $λ^2$. Improved result for the local density of states is obtained by self-consistent second-order strong-coupling expansion and continued fraction resummation.

cond-mat.str-el↗

arXiv2015

Spin susceptibility of Anderson impurities in arbitrary conduction bands

Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $χ_{\textrm{imp}}$ to susceptibility, defined originally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $χ_{\textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility $χ_{\textrm{loc}}$ and to compare them with $χ_{\textrm{imp}}$ obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in $χ_{\textrm{imp}}$ are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding $χ_{\textrm{loc}}$ less accurate than $χ_{\textrm{imp}}$, the FDM method allows a high-precision dynamical calculation of $χ_{\textrm{loc}}$ at much reduced computational cost, with an accuracy at least one order higher than $χ_{\textrm{imp}}$. Moreover, artifacts in the FDM algorithm to $χ_{\textrm{imp}}$, and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilson's definition to such cases.

cond-mat.str-el↗

arXiv2015

A New Monte Carlo Algorithm for Free Energy Calculation

We propose a new Monte Carlo algorithm for the free energy calculation based on configuration space sampling. We implement this algorithm for Ising model. Comparison with the exact free energy shows an excellent agreement. We analyse the properties of this algorithm and compares it with Wang-Landau algorithm which samples in energy space. This method is applicable to classical statistical models. The possibility of extending it to quantum systems is discussed.

cond-mat.str-el↗

arXiv2015

A Standard Basis Operator Equation of Motion Impurity Solver for Dynamical Mean Field Theory

We present an efficient impurity solver for the dynamical mean-field theory (DMFT). It is based on the separation of bath degrees of freedom into the low energy and the high energy parts. The former is solved exactly using exact diagonalization and the latter is treated approximately using Green's function equation of motion decoupling approximation. The two parts are combined coherently under the standard basis operator formalism. The impurity solver is applied to the Anderson impurity model and, combined with DMFT, to the one-band Hubbard model. Qualitative agreement is found with other well established methods. Some promising features and possible improvements of the present solver are discussed.

cond-mat.str-el↗

arXiv2013

Cluster mean-field theory study of $J_{1}-J_{2}$ Heisenberg model on a square lattice

We study the spin-1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size $L$ to infinity, we obtain accurate phase boundaries $J_{2}^{c1} \approx 0.42$ (between the N$\acute{e}$el antiferromagnetic phase and nonmagnetic phase), and $J_{2}^{c2} \approx 0.59$ (between nonmagnetic phase and the collinear antiferromagnetic phase). The transitions are identified unambiguously as second order at $J_{2}^{c1}$ and first order at $J_{2}^{c2}$. At finite temperature, we present a complete phase diagram with stable, meta-stable and unstable states near $J_{2}^{c2}$, being relevant to that of the anisotropic $J_1-J_2$ model. The uniform as well as staggered magnetic susceptibilities are also discussed.

cond-mat.str-el↗

arXiv2013

Local Entanglement Entropy at the Mott Metal-Insulator Transition in Infinite Dimensions

We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S-Sc \propto α\log_{2}[(1/2-Dc)/Dc](U-Uc), with Dc the double occupancy at Uc and α< 0 being different on two sides of the transition.

cond-mat.str-el↗

arXiv2012

Scaling Analysis in the Numerical Renormalization Group Study of the Sub-Ohmic Spin-Boson Model

The spin-boson model has nontrivial quantum phase transitions in the sub-Ohmic regime. For the bath spectra exponent $0 \leqslant s<1/2$, the bosonic numerical renormalization group (BNRG) study of the exponents $β$ and $δ$ are hampered by the boson state truncation which leads to artificial interacting exponents instead of the correct Gaussian ones. In this paper, guided by a mean-field calculation, we study the order parameter function $m(τ=α-α_c, ε, Δ)$ using BNRG. Scaling analysis with respect to the boson state truncation $N_{b}$, the logarithmic discretization parameter $Λ$, and the tunneling strength $Δ$ are carried out. Truncation-induced multiple-power behaviors are observed close to the critical point, with artificial values of $β$ and $δ$. They cross over to classical behaviors with exponents $β=1/2$ and $δ=3$ on the intermediate scales of $τ$ and $ε$, respectively. We also find $τ/Δ^{1-s}$ and $ε/Δ$ scalings in the function $m(τ, ε, Δ)$. The role of boson state truncation as a scaling variable in the BNRG result for $0 \leqslant s<1/2$ is identified and its interplay with the logarithmic discretization revealed. Relevance to the validity of quantum-to-classical mapping in other impurity models is discussed.

cond-mat.str-el↗

arXiv2010

Simulation of the spin-boson model with superconducting phase qubit coupled to a transmission line

Based on the rapid experimental developments of circuit QED, we propose a feasible scheme to simulate a spin-boson model with the superconducting circuits, which can be used to detect quantum Kosterlitz-Thouless (KT) phase transition. We design the spin-boson model by using a superconducting phase qubit coupled with a semi-infinite transmission line, which is regarded as bosonic reservoir with a continuum spectrum. By tuning the bias current or the coupling capacitance, the quantum KT transition can be directly detected through tomography measurement on the states of the phase qubit. We also estimate the experimental parameters using numerical renormalization group method.

quant-ph↗

arXiv2010

Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents $β$ and $δ$ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states $N_{b}$. We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in $0 1/2$, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.

cond-mat.str-el↗

arXiv2010

Interacting Dirac Fermions on Honeycomb Lattice

We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (CDMFT) combined with continuous time quantum Monte Carlo simulation (CTQMC). A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. We demonstrate that the non-local spatial correlations play a vital role in the Mott transition on the honeycomb lattice. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.

cond-mat.str-el↗

arXiv2009

Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry in the 2D Hubbard model

The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.

cond-mat.str-el↗

arXiv2009

Dynamical Mean Field Theory for the Bose-Hubbard Model

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $μ/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.

cond-mat.quant-gas↗

arXiv2009

Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that such a mapping fails for the sub-ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to have an upper-critical dimension at s = 1/2, with mean-field transition behavior controlled by a non-interacting fixed point for 0 < s < 1/2. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.

cond-mat.stat-mech↗

arXiv2008

Conductance plateau in quantum spin transport through an interacting quantum dot

Quantum spin transport is studied in an interacting quantum dot. It is found that a conductance "plateau" emerges in the non-linear charge conductance by a spin bias in the Kondo regime. The conductance plateau, as a complementary to the Kondo peak, originates from the strong electron correlation and exchange processes in the quantum dot, and can be regarded as one of the characteristics in quantum spin transport.

cond-mat.mes-hall↗

arXiv2006

Signatures of a Noise-Induced Quantum Phase Transition in a Mesoscopic Metal Ring

We study a mesoscopic ring with an in-line quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with $ω^s$ spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of ohmic ($s=1$) and subohmic ($s=1/2$) noise.

cond-mat.mes-hall↗