I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local fermions. This construction yields the complete spectrum of the Hamiltonian and an associated classical transfer matrix. The spatially uniform system is gapless with dynamical critical exponent z=3/2, while staggering the couplings gives a more conventional free-fermion model with an Ising transition. The Hamiltonian is equivalent to that of a spin-1/2 chain with next-nearest-neighbour interactions, and has a supersymmetry generated by a sum of fermion trilinears. The supercharges are part of a large non-abelian symmetry algebra that results in exponentially large degeneracies. The model is integrable for either open or periodic boundary conditions but the free-fermion construction only works for the former, while for the latter the extended symmetry is broken and the degeneracies split.
Construction and simulability of quantum circuits with free fermions in disguise
Università di Bologna and INFN, Sezione di Bologna（博洛尼亚大学及意大利国家核物理研究所博洛尼亚分部）；Laboratoire de Probabilités, Statistique et Modélisation & CNRS, Université Paris Cité, Sorbonne Université Paris（巴黎概率、统计与建模实验室及法国国家科学研究中心、巴黎西岱大学、索邦巴黎大学）
The University of Tokyo（东京大学）；RIKEN iTHEMS（理化学研究所 iTHEMS）；ELTE Eötvös Loránd University（罗兰大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究网络温格物理研究中心）
The University of Tokyo（东京大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所前沿研究研究院）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of anticommutation relations between the Pauli terms in $H$ in a given basis. Specifically, when $G$ is (even-hole, claw)-free, we construct an explicit free-fermion solution for $H$ using only this structure of $G$, even when no Jordan-Wigner transformation exists. The solution method is generic in that it applies for any values of the couplings. This mapping general…
It is widely believed that the spectral gap above the Fermi sea ground state of lattice free fermions is stable against generic weak interactions. Quite recently, Hastings presented a new interesting idea to prove the stability for Majorana free fermions. He ingeniously used Majorana fermions so that the unperturbed Hamiltonian of the free fermion part is mapped into a frustration-free form. In this paper, we refine Hastings's argument, and give a complete proof of the stability of the spectral gap above the Fermi sea ground state against generic weak interactions for generic lattice free ferm…
The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a positive contraction acting on a "doubled" one-particle space with an additional structure defines a unique PfPP. Recently, Olshanski inverted the direction from free fermions to DPPs, proposed a scheme to construct a fermionic state from a quasi-invariant probability measure, and introduced the notion of perfectness of a probability measure. We propose a method t…
We provide further analytical insights into the newly established noninteracting (free-fermion) Page curve, focusing on both the kinematic and dynamical aspects. First, we unveil the underlying canonical typicality and atypicality for random free-fermion states. The former appears for a small subsystem and is exponentially weaker than the well-known result in the interacting case. The latter explains why the free-fermion Page curve differs remarkably from the interacting one when the subsystem is macroscopically large, i.e., comparable with the entire system. Second, we find that the free-ferm…
The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper [Phys. Rev. B 95, 165101 (2017)]. In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entan…
We study the waiting-time distributions (WTDs) of quantum chains coupled to two Lindblad baths at each end. Our focus is on free fermion chains, where we derive closed-form expressions in terms of single-particle matrices, allowing one to study arbitrarily large chain sizes. In doing so, we also derive formulas for 2-point correlation functions involving non-Hermitian propagators.
We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is shown that logarithmic behavior holds if the two parts are conformally critical. In other cases, area law holds with abundant convergence behaviors. In particular, when XX chain at Lifshitz point is connected with a conformally or Lifshitz critical part, entanglement entropy converges algebraically with a fractional subleading index.
The University of Tokyo（东京大学）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Hong Kong University of Science and Technology（香港科技大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））
As an intrinsically-unbiased approach, quantum Monte Carlo (QMC) is of vital importance in understanding correlated phases of matter. Unfortunately, it often suffers notorious sign problem when simulating interacting fermion models. Here, we show for the first time that there exist interacting fermion models whose sign problem becomes less severe for larger system sizes and eventually disappears in the thermodynamic limit, which we dub as "asymptotic sign free". We demonstrate asymptotically-free sign in determinant QMC for various interacting models. Moreover, based on renormalization-group-l…
