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arXiv:1812.01045 · Physical review. B./Physical review. B

First-order topological quantum phase transition in a strongly correlated ladder

Simone Barbarino, Giorgio Sangiovanni, Jan Carl Budich

Published Feb 27, 2019• 24 citations
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Abstract

We report on the discovery of a quantum tricritical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system. Specifically, we study a fermionic four-leg ladder supporting a symmetry-protected topological insulator phase in the presence of on-site interaction, which is driven towards a trivial gapped phase by a nearest-neighbor interaction. Based on DMRG simulations, we show that, as a function of the interaction strength, the phase transition between the topological and the trivial phase switches from being continuous to exhibiting a first-order character. Remarkably, the QTP as well as the first-order character of the topological transition in the strongly correlated regime are found to clearly manifest in simple local observables.

DOI
10.1103/physrevb.99.075158

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We report on the discovery of a quantum tricritical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system. Specifically, we study a fermionic four-leg ladder supporting a symmetry-protected topological insulator phase in the presence of on-site interaction, which is driven towards a trivial gapped phase by a nearest-neighbor interaction. Based on DMRG simulations, we show that, as a function of the interaction strength, the phase transition between the topological and the trivial phase switches from being continuous to exhibiting a first-order character. Remarkably, the QTP as well as the first-order character of the topological transition in the strongly correlated regime are found to clearly manifest in simple local observables.
Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.
We introduce a two-ladder lattice model with interacting Majorana fermions that could be realized on the surfaces of a topological insulator film. We study this model with a combination of analytical and numerical techniques, and we find a phase diagram that features both gapless and gapped phases as well as interesting phase transitions including a quantum critical point in the tricritical Ising (TCI) universality class. The latter occurs at an intermediate-coupling strength at a meeting point of a first-order transition line and an Ising critical line, and it is known to be described by a superconformal field theory with central charge c=710c=\frac{7}{10}c=107​. We discuss the experimental feasibility of constructing the model and tuning parameters to the vicinity of the TCI point where signatures of the elusive supersymmetry can be observed.
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0T=0T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.
We investigate the two-leg Hubbard model with diagonal hopping to explore the interplay between geometrical frustration and strong electron-electron interactions. Using the Density Matrix Renormalization Group (DMRG) method, we demonstrate the emergence of a topological Haldane phase, which results explicitly from the complementary effects of diagonal hopping-induced frustration and strong on-site Coulomb repulsion. The topological phase transition from a trivial insulator to the nontrivial Haldane phase is characterized by significant changes in magnetic properties, edge correlations, and the appearance of a nonzero string order parameter. Furthermore, we confirm the topological nature of this phase through a detailed analysis of the spin gap and entanglement spectrum, demonstrating clear signatures of symmetry-protected topological order.
We show that a one-dimensional lattice of spinless fermions can undergo a topological phase transition only due to the effect of interaction. By allowing a dimerized interaction among the particles we show that the system exhibits a symmetry protected topological phase which does not exist in the absence of interaction and the system is a gapless state. The nontrivial topological character appears due to the onset of two degenerate bond-order phases as a function of dimerized interaction which are found to be topologically distinct from each other. As a result a topological phase transition occurs between these bond-order phases through a gap closing point. However, in the limit of strong interaction, the topologically distinct bond-order phases are separated from each other through a gapped charge density wave phase possessing a local antiferromagnetic order. We characterize this emergent topological nature by the edge states, Berry phase, and a nonlocal string order parameter and provide possible experimental signatures in terms of Thouless charge pumping and density-density correlation.
The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd ``axionic'' insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.