Controllable Incremental Algorithm for Entanglement Entropy and Other Observables with Exponential Variance Explosion in Many-Body Systems

Researchers in the field of physical science are continuously searching for universal features in strongly interacting many-body systems. However, these features can often be concealed within highly complex observables, such as entanglement entropy (EE). The non-local nature of these observables makes them challenging to measure experimentally or evaluate numerically. Therefore, it is of utmost importance to develop a reliable and convenient algorithm that can accurately obtain these complex observables. In this paper, with help of quantum Monte Carlo (QMC), we reveal that the statistical variance of EE exponentially explodes with respect to the system size, making the evaluation of EE inaccurate. We further introduce an incremental algorithm based on the framework of QMC to solve this conundrum. The total number of our incremental processes can be quantitatively determined and reasonably adjusted, making it easy to control the precision in practice. We demonstrate the effectiveness and convenience of our incremental algorithm by using it to obtain the highly accurate EE of a 2D Hubbard model as an example. Additionally, our algorithm can be potentially generalized to calculate other numerically statistically unstable observables with exponential variance growth, such as the entanglement spectrum and topological entanglement negativity of correlated boson/spin and fermion systems, as well as other general functions of determinants of Green's functions in interacting fermions. Accurately measuring these complex observables has the potential to inspire the development of physical theories and guide the direction of experiments.Comment: 5 pages, 3 figure

Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition

Inspired by our recent works[1, 2] of SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase digram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases such as the Dirac semimetal, the antiferromagnetic Mott insulator, valence bond solid (VBS) and the Dirac spin liquid and phase transitions including the Gross-Neveu chiral transitions with emergent continuous symmetry, the deconfined quantum criticality and the first order transition between interaction-driven columnar VBS and plaquette VBS. These rich phenomena coming from the simple-looking lattice models, firmly convey the message that the interplay between the $SU(N)$ Dirac fermions -- with enhanced internal symmetries -- and extended plaquette interactions -- beyond the on-site Hubbard type -- is the new playground to synthesise novel highly entangled quantum matter both at the model level and with experimental feasibilities.Comment: 9 pages, 7 figure

Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition

Lately there are many SLAC fermion investigations on the (2+1)D Gross-Neveu criticality of a single Dirac cone [1,2]. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the non-interacting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP) -- which a priori requires short-range interaction -- has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local $\pi$-flux Hubbard model on the square lattice. In particular, we find the antiferromagnetic long-range order in the SLAC fermion model has a finite temperature continuous phase transition, which violates the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous $SU(2)$ symmetry. These unusual results proclaim caution on the interpretation of the quantum phase transition in SLAC fermion model as that of GN-QCP with short-range interaction

Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities

We investigate the ground state phase diagram of an extended Hubbard model with $\pi$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents $\eta_\text{VBS}=0.6(1)$ and $\eta_\text{AF}=0.58(3)$ at deconfined quantum critical point satisfy the CFT Bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and close at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum Moir\'e systems, are discussed.Comment: 6+2 pages, 5+2 figure

Intragraft Selection of the T Cell Receptor Repertoire by Class I MHC Sequences in Tolerant Recipients

Background: Allograft tolerance of ACI (RT1 a) recipients to WF (RT1 u) hearts can be induced by allochimeric class I MHC molecules containing donor-type (RT1A u) immunogenic epitopes displayed on recipient-type (RT1A a) sequences. Here, we sought the mechanisms by which allochimeric sequences may affect responding T cells through T cell receptor (TCA) repertoire restriction. Methodology/Principal Findings: The soluble [a1h u]-RT1.A a allochimeric molecule was delivered into ACI recipients of WF hearts in the presence of sub-therapeutic dose of cyclosporine (CsA). The TCR Vb spectrotyping of the splenocytes and cardiac allografts showed that the Vb gene families were differentially expressed within the TCR repertoire in allochimericor high-dose CsA-treated tolerant recipients at day +5 and +7 of post-transplantation. However, at day 30 of posttransplantation the allochimeric molecule-treated rats showed the restriction of TCR repertoire with altered dominant size peaks representing preferential clonal expansion of Vb7, Vb11, Vb13, Vb 14, and Vb15 genes. Moreover, we found a positive correlation between the alteration of Vb profile, restriction of TCR repertoire, and the establishment of allograft tolerance. Conclusions: Our findings indicate that presentation of allochimeric MHC class I sequences that partially mimic donor an