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We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…
The classification of symmetry-protected topological (SPT) phases in one dimension has been recently achieved, and had a fundamental impact in our understanding of quantum phases in condensed matter physics. In this framework, SPT phases…
Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D…
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally.…
Symmetry-protected topological (SPT) phases of matter have been the focus of many recent theoretical investigations, but controlled mechanisms for engineering them have so far been elusive. In this work, we demonstrate that by driving…
We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two…
We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom…
We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between $x$ and $z$ pseudospin components along both the ladder legs and on the rungs. We show that it is equivalent to an…
A nonlocal string order parameter detecting topological order and deconfinement has been proposed by Fredenhagen and Marcu (FM). However, due to the lack of exact internal symmetries for lattice models and the nonlinear dependence of the FM…
These lecture notes explain the classification of some simple fermionic topological phases of matter in a pedestrian manner, with an aim to be maximally pedagogical = doing things in excruciating detail. We focus on a many-body perspective,…
The ground state of the $S=1$ antiferromagnetic Heisenberg chain belongs to the Haldane phase -- a well known example of symmetry-protected topological phase. A staggered field applied to the $S=1$ antiferromagnetic chain breaks all the…
We have studied the excitation spectrum of the $S=1/2$ quantum spin ladder with staggered dimerization by dimer series expansions, diagrammatic analysis of an effective interacting Bose gas of local triplets, and exact diagonalization of…
We study critical phenomena of the SU(3) symmetric spin-1 chains when adding the SU(3) asymmetric term. To investigate such system, we numerically diagonalize the Dimer-Trimer (DT) model Hamiltonian around the SU(3) symmetric point, named…
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting…
The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models.…
We explore the ground-state phase diagram of a Heisenberg spin chain coupled locally to optical phonons (bond coupling), using large-scale density matrix renormalization group calculations and an extended perturbative analysis. For the…
Topological phase transitions in free fermion systems can be characterized by closing of single-particle gap and change in topological invariants. However, in the presence of electronic interactions, topological phase transitions are more…
Here we study the emergence of different Symmetry-Protected Topological (SPT) phases in a spin-2 quantum chain. We consider a Heisenberg-like model with bilinear, biquadratic, bicubic, and biquartic nearest-neighbor interactions, as well as…
We show that a quadratic system of pseudofermions, with tunable fractionalised statistics, can host a rich phase diagram on a one dimensional chain with nearest and next nearest neighbor hopping. Using a combination of numerical and…
It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) on the…