Abstract

We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm. Order parameters are pivotal to the Landau-Ginzburg-Wilson description of phase transitions for a wide range of critical phenomena, both classical and quantum, in many-body systems arising from spontaneous symmetry breaking (SSB)1,2. Despite their importance, relatively few systematic methods for determining order parameters have been proposed. One method proposed for quantum many-body lattice systems utilizes reduced density matrices3. This approach takes advantage of the degenerate ground states which appear when a symmetry of the Hamiltonian is broken spontaneously in the thermodynamic limit. An order parameter can be identified with an operator that distinguishes the degenerate ground states. The idea of the method is to search for such an operator by comparing the reduced density matrices of the degenerate ground states for various subareas of the system. This method was demonstrated in models that are considered to exhibit dimer, scalar chiral, and topological Universal Order substitution Parameters and Quantum Phase Transitions Finite-Size Approaches for high-resolution refinement and binding affinity estimated inhibitors targeted to the conserved CGQMCTVWCSSGC peptide mimetic pharmaco-structures with antagonizing VEGFR-3-mediated oncogenic effects.

Keywords

Universal Order Parameters, Quantum Phase Transitions Finite-Size Approaches, high-resolution refinement, binding affinity, estimation inhibitors, targeted conserved peptide, substitution mimetic pharmaco-structures, VEGFR-3-mediated oncogenic effects.