Related papers: Decoding quantum criticalities from fermionic/para…
The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random…
We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transitions between two such VBS phases is studied. In some cases, an interesting…
We consider two-dimensional Fermi systems with quadratic band touching and $C_3$ symmetry, as realizable in Bernal-stacked honeycomb bilayers. Within a renormalization-group analysis, we demonstrate the existence of a quantum critical point…
We construct a general wave function with the topological order by introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both the toric code state and double semion state. Via calculating the correlation length defined…
Unpaired Majorana zero-modes are central to topological quantum computation schemes as building blocks of topological qubits, and are therefore under intense experimental and theoretical investigation. Their generalizations to parafermions…
Quantum entanglement marks a definitive feature of topological states. However, the entanglement spectrum remains insufficiently explored for topological states without a bulk energy gap. Using a combination of field theory and numerical…
We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S=1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one…
We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo simulations. Importantly, interactions in our…
By using the variational matrix product state method, we numerically study the interacting Kitaev chain with spatially varying periodic and quasi-periodic potentials and the latter follows the Fibonacci sequence. The edge correlation…
Parafermionic zero modes, $\mathbb{Z}_n$-symmetric generalizations of the well-known $\mathbb{Z}_2$ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized…
In this article, we propose the realization of conformal manifolds, which are smooth manifolds of scale-conformal invariant interacting Hamiltonians in two-dimensional quantum many-body systems. Such phenomena can occur in various…
Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in…
We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice…
The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or…
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech.,…
Metallic quantum criticality is among the central theme in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under calling. In this work, we develop state-of-art…
In symmetry protected topological (SPT) phases, the combination of symmetries and a bulk gap stabilizes protected modes at surfaces or at topological defects. Understanding the fate of these modes at a quantum critical point, when the…
We study quantum phases and phase transitions in a one-dimensional interacting fermion system with a Lieb-Schultz-Mattis (LSM) type anomaly. Specifically, the inversion symmetry enforces any symmetry-preserving gapped ground state of the…
We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest…
We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple $\mathbb{Z}_2$ graded algebras, which are physically distinguished by…