Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach

We propose a general extended coherent state approach to the qubit (or fermion) and multi-mode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents $s<1/2$ can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.Comment: 4 pages, 3 figure

Quantum phase transitions in coupled two-level atoms in a single-mode cavity

The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at the strong interatomic interaction. Similar to the original Dicke model, this system exhibits a second-order quantum phase transition from the normal to the superradiant phases. Finite-size scaling for several observables, such as the average fidelity susceptibility, the order parameter, and concurrence are performed for different interatomic interactions. The obtained scaling exponents suggest that interatomic interactions do not change the universality class.Comment: 13 pages, 5 figure

Accurate numerical solution to the finite-size Dicke model

By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence are analyzed. The existing discrepancy for the scaling exponent of the concurrence is reconciled.Comment: 4 pages, 5 figures. Phys. Rev. A (in press, a Rapid Communication

WheaCha: A Method for Explaining the Predictions of Models of Code

Attribution methods have emerged as a popular approach to interpreting model predictions based on the relevance of input features. Although the feature importance ranking can provide insights of how models arrive at a prediction from a raw input, they do not give a clear-cut definition of the key features models use for the prediction. In this paper, we present a new method, called WheaCha, for explaining the predictions of code models. Although WheaCha employs the same mechanism of tracing model predictions back to the input features, it differs from all existing attribution methods in crucial ways. Specifically, WheaCha divides an input program into "wheat" (i.e., the defining features that are the reason for which models predict the label that they predict) and the rest "chaff" for any prediction of a learned code model. We realize WheaCha in a tool, HuoYan, and use it to explain four prominent code models: code2vec, seq-GNN, GGNN, and CodeBERT. Results show (1) HuoYan is efficient - taking on average under twenty seconds to compute the wheat for an input program in an end-to-end fashion (i.e., including model prediction time); (2) the wheat that all models use to predict input programs is made of simple syntactic or even lexical properties (i.e., identifier names); (3) Based on wheat, we present a novel approach to explaining the predictions of code models through the lens of training data