arXiv subjects

Eric Bobrow

Publications and source records attributed to Eric Bobrow.

7 recordsLinked to original sources

arXiv2024

Requirements for building effective Hamiltonians using quantum-enhanced density matrix downfolding

Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of difficult-to-quantify systematic errors attendant to sampling the observables of quantum many-body systems on an approximate low-energy subspace. We propose a hybrid quantum-classical protocol for circumventing this limitation, relying on the prospective ability of quantum computers to efficiently prepare and sample from states in well-defined low-energy subspaces with systematically improvable accuracy. We introduce three requirements for when this is possible, including a notion of compressibility that quantifies features of Hamiltonians and low-energy subspaces thereof for which quantum DMD might be efficient. Assuming that these requirements are met, we analyze design choices for our protocol and provide resource estimates for implementing quantum-enhanced DMD on both the doped 2-D Fermi-Hubbard model and an ab initio model of a cuprate superconductor.

quant-ph↗

arXiv2022

Monopole Superconductivity in Magnetically Doped Cd$_3$As$_2$

When superconducting pairing occurs between Fermi surfaces with different Chern numbers, the Cooper pairs possess nontrivial pair Berry phase, which enforces pairing gap nodes. The resulting pairing order is further distinguished from the familiar $s$-, $p$-, and $d$-wave pairing orders by a nonzero pair monopole charge and is described by monopole harmonics. To date, this exotic monopole pairing order is yet to be achieved experimentally. We therefore study the magnetically doped Dirac semimetal Cd$_3$As$_2$ as a candidate material for realizing monopole superconductivity with pair monopole charges $q_p=1$ or $2$, depending on the chemical potential. For each case of pair monopole charge, we explore representatives of uniform pairing orders in all allowed irreducible representations of the $C_{4h}$ symmetry of magnetically doped Cd$_3$As$_2$. We demonstrate the distinctions in the monopole analogs of different higher partial wave superconducting orders that result from the combination of topological Fermi surfaces of higher Chern number and crystalline symmetry. In all cases, the patterns of the superconducting phase winding around a Fermi surface are constrained by the topologically invariant total winding number, which depends only on the pair monopole charge and requires nodes in the $q_p\neq 0$ superconducting order. Our work can guide further experimental investigation of monopole orders in the topological semimetal Cd$_3$As$_2$ and can be generalized to other materials with Fermi surfaces of higher Chern number, which enforce monopole pairing order in higher partial waves, such as the monopole analog of $f$-wave pairing.

cond-mat.supr-con↗

arXiv2020

Robust Flat Bands with Tunable Energies in Honeycomb Superlattices

Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructive interference in real space that give rise to the flat bands robust against long range hoppings.

cond-mat.mes-hall↗

arXiv2020

Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band

By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a $p_x$, $p_y$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.

cond-mat.str-el↗

arXiv2018

Monopole Charge Density Wave States in Weyl Semimetals

We study a new class of topological charge density wave states exhibiting monopole harmonic symmetries. The density-wave ordering is equivalent to pairing in the particle-hole channel due to Fermi surface nesting under interactions. When electron and hole Fermi surfaces carry different Chern numbers, the particle-hole pairing exhibits a non-trivial Berry phase inherited from band structure topology independent of concrete density-wave ordering mechanism. The associated density-wave gap functions become nodal, and the net nodal vorticity is determined by the monopole charge of the pairing Berry phase. The gap function nodes become zero-energy Weyl nodes of the bulk spectra of quasi-particle excitations. These states can occur in doped Weyl semimetals with nested electron and hole Fermi surfaces enclosing Weyl nodes of the same chirality in the weak coupling regime. Topologically non-trivial low-energy Fermi arc surface states appear in the density-wave ordering state as a consequence of the emergent zero-energy Weyl nodes.

cond-mat.str-el↗

arXiv2018

Exact Results on Itinerant Ferromagnetism and the 15-puzzle Problem

We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem of ferromagnetism is extended to all non-separable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a $U\to\infty$ Hubbard model with one hole away from the half filling on a 2D honeycomb lattice or a 3D diamond lattice is fully spin-polarized. Furthermore, the condition of connectivity for $N$-component fermions is presented, and Nagaoka's theorem is also generalized to $SU(N)$-symmetric fermion systems on non-separable graphs.

cond-mat.str-el↗

arXiv2018

Stability of the Nagaoka-type Ferromagnetic State in a $t_{2g}$ Orbital System on a Cubic Lattice

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three dimensional $t_{2g}$-orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is valid for arbitrary values of the ferromagnetic Hund's coupling $J>0$ and inter-orbital repulsion $V\ge 0$. The stability of the Nagaoka-type state at finite electron densities with respect to a single spin-flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the $t_{2g}$-orbital materials.

cond-mat.str-el↗