Jordan Gaines | Searcharxiv

arXiv2025

Spin-Chain Multichannel Kondo Model via Image Impurity Boundary Condition

One of the signature observables for the electronic multichannel Kondo model is the impurity entropy, which was found in $J_1$-$J_2$ Heisenberg chains with the open boundary condition (OBC) and periodic boundary condition (PBC), for the one-channel and two-channel cases respectively. However, it is not clear how to generalize OBC and PBC in Heisenberg chains to find the multichannel Kondo impurity entropy with more than two channels. In this paper, we demonstrate that the correct boundary condition for realizing multichannel Kondo physics in Heisenberg chains is the image impurity boundary condition (IIBC) which preserves reflection symmetry and yields the expected impurity entropy, $\ln[(\sqrt{5}+1)/2]$ for the three-channel case and $\ln\sqrt{3}$ for the four-channel case. Moreover, the IIBC reduces to OBC for the one-channel case and to PBC for the two-channel case. With IIBC, the finite-size scaling of the impurity entropy and the total impurity spin match the finite-temperature corrections in the electronic multichannel Kondo model. Additionally, we show dependence of the impurity entropy, the total impurity spin, and their scaling behaviors on the XXZ anisotropy $\Delta$ (equivalently the Luttinger liquid parameter), revealing impurity physics in a multichannel Luttinger liquid.

cond-mat.str-el↗

arXiv2024

Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix

Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant computational overhead, fermionic quantum hardware, such as fermion atom arrays, were proposed as a more efficient platform. In this context, we here study the many-body entanglement structure of fermionic $N$-particle states by concentrating on $M$-body reduced density matrices (DMs) across various bipartitions in Fock space. The von Neumann entropy of the reduced DM is a basis independent entanglement measure which generalizes the traditional quantum chemistry concept of the one-particle DM entanglement, which characterizes how a single fermion is entangled with the rest. We carefully examine upper bounds on the $M$-body entanglement, which are analogous to the volume law of conventional entanglement measures. To this end we establish a connection between $M$-body reduced DM and the mathematical structure of hypergraphs. Specifically, we show that a special class of hypergraphs, known as $t$-designs, corresponds to maximally entangled fermionic states. Finally, we explore fermionic many-body entanglement in random states. We semianalytically demonstrate that the distribution of reduced DMs associated with random fermionic states corresponds to the trace-fixed Wishart-Laguerre random matrix ensemble. In the limit of large single-particle dimension $D$ and a non-zero filling fraction, random states asymptotically become absolutely maximally entangled.

quant-ph↗