Quantum Phase Transitions in Matrix Product Systems

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of “conventional” QPTs.

Figure 1

Energies for the ground and first excited state as a function of $g$. In contrast to other QPTs the GS energy of a MPS Hamiltonian remains (by construction) analytic at the QPT point $g=g_c$. Nevertheless, the spectral gap vanishes and the correlation length diverges. Moreover, the nonanalytic change of the GS at $g_c$ is reflected by an observable nonanalyticity of certain local expectation values.