Quantum Phase Transitions: A Network Approach

David L. Vargas, Lincoln D. Carr

Lincoln D. Carr, Marc Andrew Valdez, Daniel Jaschke +3 more

Joydip Ghosh, Barry C. Sanders

We devise a scalable scheme for simulating a quantum phase transition from paramagnetism to frustrated magnetism in a superconducting flux-qubit network, and we show how to characterize this system experimentally both macroscopically and microscopically. The proposed macroscopic characterization of the quantum phase transition is based on the transition of the probability distribution for the spin-network net magnetic moment with this transition quantified by the difference between the Kullback–Leibler divergences of the distributions corresponding to the paramagnetic and frustrated magnetic phases with respect to the probability distribution at a given time during the transition. Microscopic characterization of the quantum phase transition is performed using the standard local-entanglement-witness approach. Simultaneous macro and micro characterizations of quantum phase transitions would serve to verify a quantum phase transition in two ways especially in the quantum realm for the classically intractable case of frustrated quantum magnetism.

Sheng-Hao Li, Yuanyuan Wu, Fei Xiong

With the deepening of people's understanding of quantum phase transitions, various efficient numerical algorithms have developed rapidly. It is necessary to develop tensor network algorithms to efficiently generate the ground state wave function of quantum many-body system and then calculate the ground state fidelity per site. This mini review article aims to discusses the tensor network algorithm for studying 2-dimensional quantum lattice systems, namely projected entangled pair state, and introduce how to characterize phase transitions in quantum many-body systems from a novel perspective-fidelity. It includes the wave function updating of projected entangled pair state and the tensor network contraction scheme, which can be used to calculate the ground-state fidelity per site of the quantum system, and the phase diagram of the ground-state can be determined without any knowledge of the order of the 2-dimensional quantum system, thus indicating that tensor network algorithms can provide a means to describe quantum phase transitions.

Guin-Dar Lin, Christopher R. Monroe, L.-M. Duan

Sharp quantum phase transitions typically require a large system with many particles. Here we show that, for a frustrated fully connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility of observing sharp quantum phase transitions in a system of just a few trapped ion spins.