Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories

Abstract

In a bipartite set-up, the vacuum state of a free Bosonic scalar field is entangled in real space and satisfies the area-law— entanglement entropy scales linearly with area of the boundary between the two partitions. In this work, we show that the area law is violated in two spatial dimensional model Hamiltonian having dynamical critical exponent z = 3. The model physically corresponds to next-to-next-to-next nearest neighbour coupling terms on a lattice. The result reported here is the first of its kind of violation of area law in Bosonic systems in higher dimensions and signals the evidence of a quantum phase transition. We provide evidence for quantum phase transition both numerically and analytically using quantum Information tools like entanglement spectra, quantum fidelity, and gap in the energy spectra. We identify the cause for this transition due to the accumulation of large number of angular zero modes around the critical point which catalyses the change in the ground state wave function due to the next-to-next-to-next nearest neighbor coupling. Lastly, using Hubbard-Stratanovich transformation, we show that the effective Bosonic Hamiltonian can be obtained from an interacting fermionic theory and provide possible implications for condensed matter systems.

Role of spatial higher order derivatives in momentum space entanglement

“…The importance of the higher derivative spatial terms were studied in Refs. [18,19] and can be used to understand some quantum phase transitions. Unlike the Wilsonian type renormalization [10][11][12], the higher derivative terms introduce Next-to-Next-to-Next interaction in the lattice.…”

Log to log-log crossover of entanglement in $(1+1)-$ dimensional massive scalar field

“…Given a particular form of coupling matrix K, this can be obtained through a well-known procedure [3,17]. The eigenvalues can then be used to visualize the entanglement spectrum [12,15] of the reduced subsystem. Subsequently, they can also be used to calculate the entanglement entropy of the subsystem, which is a popular measure for such correlations.…”

“…For instance, in the case of fractional quantum Hall states, the low-lying levels of entanglement spectrum capture information about the edge modes that help identify topological order, as well as the CFT associated with it [12,13]. The difference between the lowest two levels in the spectrum, known as the "entanglement gap", further contains signatures of symmetry-breaking and quantum phase transitions in many-body systems [12,14,15]. Closing of this gap is found to be associated with quantum criticality [16].…”

Ground-state fidelity at first-order quantum transitions

“…In quantum many-body systems, the establishment of a non-analytic behavior has been exploited to evidence CQTs in several different contexts, which have been deeply scrutinized both analytically and numerically. We quote, for example, free-fermion models [14][15][16][17][18], interacting spin [19][20][21][22][23][24][25] and particle models [26][27][28][29][30][31][32], as well as systems presenting peculiar topological [33][34][35] and nonequilibrium steady-state transitions [36,37]. However a characterization of first-order QTs (FOQTs) in this context is still missing, despite the fact that they are of great phenomenological interest.…”