Characteristic quantum phase in Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies.

We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.

Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer's Principle.

Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer's principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models-the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.

Critical exponents of block-block mutual information in one-dimensional infinite lattice systems.

We study the mutual information between two lattice blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum q-state Potts model and transverse-field spin-1/2 XY model are considered numerically by using the infinite matrix product state approach. As a system parameter varies, block-block mutual information exhibit singular behaviors that enable us to identify the critical points for the quantum phase transitions. As happens with von Neumann entanglement entropy of single block, at critical points, block-block mutual information for two adjacent blocks show a logarithmic leading behavior with increasing the size of the blocks, which yields the central charge c of the underlying conformal field theory, as it should be. It seems that two disjoint blocks show a similar logarithmic growth of the mutual information as a characteristic property of critical systems but the proportional coefficients of the logarithmic term are very different from the central charges. As the separation between the two lattice blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size ℓ, the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for the different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller. We discuss a relation between the exponents of block-block mutual information and correlation with the Shatten one-norm of block-block correlation.

Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.

We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).