Ning-Hua Tong

Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model.

We describe the generalization of Wilsons numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.

Numerical Renormalization Group for Quantum Impurities in a Bosonic Bath

We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and sub-Ohmic cases. We present various results for static as well as dynamic quantities and discuss details of the numerical implementation, e.g., the discretization of a bosonic bath with arbitrary continuous spectral density, the suitable choice of a finite basis in the bosonic Hilbert space, and questions of convergence with respect to truncation parameters. The method is shown to provide high-accuracy data over the whole range of model parameters and temperatures, which are in agreement with exact results and other numerical data from the literature.

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 the naive 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) proportional, variantomega(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 display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.

Interacting Dirac fermions on honeycomb lattice

We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (DMFT) combined with continuous-time quantum Monte Carlo simulation. A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. Our results suggest that for weak interaction, the system is semimetal and the Fermi velocity keeps constant. The system undergoes a second-order Mott transition with increasing the interaction strength. We demonstrate that the nonlocal spatial correlations play a vital role in the Mott transition on the honeycomb lattice. A phase diagram of Mott transition is presented. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.

Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems

A hierarchical equations of motion based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi-liquid characteristics, achieving the accuracy of the latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the hierarchical equations of motion approach potentially useful for addressing strongly correlated lattice systems in the framework of dynamical mean-field theory.

Signatures of a noise-induced quantum phase transition in a mesoscopic metal ring.

We study a mesoscopic ring with an inline quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with omega(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 sub-Ohmic (s = 1/2) noise.

Cluster mean-field theory study of J1−J2 Heisenberg model on a square lattice

We study the spin-1/2 J1-J2 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(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.

Mott-Hubbard transition in infinite dimensions

Grazing incidence x-ray reflectivity spectra from copper/permalloy multilayers have been recorded as a function of incident x-ray energy under conditions of fixed scattering vector. From the smoothly varying part of the spectrum, it is possible separately to determine the density and composition as the energy is scanned through the K edges of the constituent elements. From the fit to model layer structures, we determine that there exists a strained layer of permalloy at the permalloy/copper interface that relaxes towards the unstrained density of permalloy on annealing. No such layer exists at the copper/permalloy interface. Cobalt doping results in the formation of a layer of mixed CoNiFe composition, rather than a single Co layer. Oscillations in the spectra above the absorption edges are analyzed in a similar manner to that for diffraction anomalous fine structure and enable the short range order within the layers to be determined. No changes are observed in the Cu or Co environments, but a reduction in the in-plane first shell distance around the Ni atoms is found on annealing.

Hierarchical equations of motion for an impurity solver in dynamical mean-field theory

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the novel HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.

Dynamics of the quantum Fisher information in a spin-boson model

The quantum Fisher information characterizes the phase sensitivity of qubits in the spin-boson model with a finite bandwidth spectrum. In contrast with Markovian reservoirs, the quantum Fisher information flows from the environments to qubits after a number of times if the bath parameter s is larger than a critical value which is related to temperature. The sudden-change behavior will happen during the evolution of the quantum Fisher information of the maximal entanglement state in the non-Markovian environments. The sudden-change times can be varied with the change of the bath parameter s. For a very large number of entangled qubits, the sudden-change behavior of the maximal quantum Fisher information can be used to characterize the existence of the entanglement. The metrology strategy based on the quantum correlated state leads to a lower phase uncertainty when compared with the uncorrelated product state.