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Register a new userCorner charge and bulk multipole moment in periodic systems
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A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an $n$-fold rotation symmetry with $n=3$, $4$, and $6$, the quadrupole moment is quantized and is independent of the spread or shape of Wannier orbitals, depending only on the location of Wannier centers of filled bands. In this case, our formula predicts the fractional part of the quadrupole moment purely from the bulk property. The system can contain many-body interactions as long as the ground state is gapped and topologically trivial in the sense it is smoothly connected to a product state limit. An extension of these results to three-dimensional systems is also discussed. In three dimensions, in general, even the fractional part of the corner charge is not fully predictable from the bulk perspective even in the presence of point group symmetry.
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Quantum entanglement is one essential element to characterize many-body quantum systems. However, so far, the entanglement measures mainly restrict to Hermitian systems. Here, we propose a natural extension of entanglement and Renyi entropies to non-Hermitian quantum systems. We demonstrate the generic entanglement and Renyi entropies capture the correct entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/Renyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/Renyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th Renyi entropy captures the expected entanglement property, whereas the traditional Renyi entropy can exhibit unnatural singularities due to its improper definition.
Recent developments in higher-order topological phases have elucidated on the relationship between nontrivial multipole moments in the bulk and the emergence of fractionally quantized charges at the boundary. Here, we put on the table a proposal of the three-dimensional octupole insulator with fractionally quantized corner charges $pm e/8$: sodium chloride, commonly known as table salt. The fractional quantization of the corner charge is unaffected by the quantum fluctuation of the electric charge per ion, as we demonstrate explicitly with ab initio calculations. We further show that the electrostatic signature of the fractional charge is well-preserved even when the ideal crystal is sprinkled with defects, and provide a systematic analysis on how the corner charge contribution could be isolated from the electric-field corrections originating from realistic surface relaxation. Our results suggest that the observation of corner charges from quantized multipole moments in solids might be around the corner.
Recent studies revealed that the electric multipole moments of insulators result in fractional electric charges localized to the hinges and corners of the sample. We here explore the magnetic analog of this relation. We show that a collinear antiferromagnet with spin $S$ defined on a $d$-dimensional cubic lattice features fractionally quantized magnetization $M_{text{c}}^z=S/2^d$ at the corners. We find that the quantization is robust even in the presence of gapless excitations originating from the spontaneous formation of the Neel order, although the localization length diverges, suggesting a power-law localization of the corner magnetization. When the spin rotational symmetry about the $z$ axis is explicitly broken, the corner magnetization is no longer sharply quantized. Even in this case, we numerically find that the deviation from the quantized value is negligibly small based on quantum Monte Carlo simulations.
The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to $S=1/2$ fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite $U$ and intersite $W_{1}$ and $W_{2}$ (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive $W_{1}>0$, the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state ($T=0$) diagram for $W_{2}leq0$ as well as finite temperature ($T>0$) phase diagrams for $W_{2}=0$ are presented. Two different types of charge order within $sqrt{3} times sqrt{3}$ unit cell can occur. At $T=0$, for $W_{2}=0$ phase separated states are degenerated with homogeneous phases (but $T>0$ removes this degeneration), whereas attractive $W_2<0$ stabilizes phase separation at incommensurate fillings. For $U/W_{1}<0$ and $U/W_{1}>1/2$ only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive $0<U/W_{1}<1/2$ the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.
We present the real-time renormalization group (RTRG) method as a method to describe the stationary state current through generic multi-level quantum dots with a complex setup in nonequilibrium. The employed approach consists of a very rudiment approximation for the RG equations which neglects all vertex corrections while it provides a means to compute the effective dot Liouvillian self-consistently. Being based on a weak-coupling expansion in the tunneling between dot and reservoirs, the RTRG approach turns out to reliably describe charge fluctuations in and out of equilibrium for arbitrary coupling strength, even at zero temperature. We confirm this in the linear response regime with a benchmark against highly-accurate numerically renormalization group data in the exemplary case of three-level quantum dots. For small to intermediate bias voltages and weak Coulomb interactions, we find an excellent agreement between RTRG and functional renormalization group data, which can be expected to be accurate in this regime. As a consequence, we advertise the presented RTRG approach as an efficient and versatile tool to describe charge fluctuations theoretically in quantum dot systems.
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