145 research outputs found
The effect of quantization on the FCIQMC sign problem
The sign problem in Full Configuration Interaction Quantum Monte Carlo
(FCIQMC) without annihilation can be understood as an instability of the
psi-particle population to the ground state of the matrix obtained by making
all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence
the sign problem, is basis dependent. In this paper we discuss the properties
of a physically important basis choice: first versus second quantization. For a
given choice of single-particle orbitals, we identify the conditions under
which the fermion sign problem in the second quantized basis of antisymmetric
Slater determinants is identical to the sign problem in the first quantized
basis of unsymmetrized Hartree products. We also show that, when the two
differ, the fermion sign problem is always less severe in the second quantized
basis. This supports the idea that FCIQMC, even in the absence of annihilation,
improves the sign problem relative to first quantized methods. Finally, we
point out some theoretically interesting classes of Hamiltonians where first
and second quantized sign problems differ, and others where they do not.Comment: 4 pages w/ 2 page appendix, 2 figures, 1 tabl
The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
We propose a topological Euler number to characterize nontrivial topological
phases of gapped fermionic systems, which originates from the Gauss-Bonnet
theorem on the Riemannian structure of Bloch states established by the real
part of the quantum geometric tensor in momentum space. Meanwhile, the
imaginary part of the geometric tensor corresponds to the Berry curvature which
leads to the Chern number characterization. We discuss the topological numbers
induced by the geometric tensor analytically in a general two-band model. As an
example, we show that the zero-temperature phase diagram of a transverse field
XY spin chain can be distinguished by the Euler characteristic number of the
Bloch states manifold in a (1+1)-dimensional Bloch momentum space
Modulation of the DNA-binding activity of Saccharomyces cerevisiae MSH2âMSH6 complex by the high-mobility group protein NHP6A, in vitro
DNA mismatch repair corrects mispaired bases and small insertions/deletions in DNA. In eukaryotes, the mismatch repair complex MSH2âMSH6 binds to mispairs with only slightly higher affinity than to fully paired DNA in vitro. Recently, the high-mobility group box1 protein, (HMGB1), has been shown to stimulate the mismatch repair reaction in vitro. In yeast, the closest homologs of HMGB1 are NHP6A and NHP6B. These proteins have been shown to be required for genome stability maintenance and mutagenesis control. In this work, we show that MSH2âMSH6 and NHP6A modulate their binding to DNA in vitro. Binding of the yeast MSH2âMSH6 to homoduplex regions of DNA significantly stimulates the loading of NHP6A. Upon binding of NHP6A to DNA, MSH2âMSH6 is excluded from binding unless a mismatch is present. A DNA binding-impaired MSH2âMSH6F337A significantly reduced the loading of NHP6A to DNA, suggesting that MSH2âMSH6 binding is a requisite for NHP6A loading. MSH2âMSH6 and NHP6A form a stable complex, which is responsive to ATP on mismatched substrates. These results suggest that MSH2âMSH6 binding to homoduplex regions of DNA recruits NHP6A, which then prevents further binding of MSH2âMSH6 to these sites unless a mismatch is present
Adiabatic perturbation theory and geometry of periodically-driven systems
We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.The authors would like to thank M. Aidelsburger, M. Atala, E. Dalla Torre, N. Goldman, M. Heyl, D. Huse, G. Jotzu, C. Kennedy, M. Lohse, T. Mori, L. Pollet, M. Rudner, A. Russomanno, and C. Schweizer for fruitful discussions. This work was supported by AFOSR FA9550-16-1-0334, NSF DMR-1506340, ARO W911NF1410540, and the Hungarian research grant OTKA Nos. K101244, K105149. M. K. was supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors are pleased to acknowledge that the computational work reported in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services. The authors also acknowledge the Research Computing Services group for providing consulting support which has contributed to the results reported within this paper. The study of the driven non-integrable transverse-field Ising model was carried out using QuSpin [185] - an open-source state-of-the-art Python package for dynamics and exact diagonalization of quantum many body systems, available to download here. (FA9550-16-1-0334 - AFOSR; DMR-1506340 - NSF; W911NF1410540 - ARO; K101244 - Hungarian research grant OTKA; K105149 - Hungarian research grant OTKA; DE-AC02-05CH11231 - Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab)https://arxiv.org/pdf/1606.02229.pd
High-precision measurements from LHC to FCC-ee
This document provides a writeup of all contributions to the workshop on
"High precision measurements of : From LHC to FCC-ee" held at CERN,
Oct. 12--13, 2015. The workshop explored in depth the latest developments on
the determination of the QCD coupling from 15 methods where high
precision measurements are (or will be) available. Those include low-energy
observables: (i) lattice QCD, (ii) pion decay factor, (iii) quarkonia and (iv)
decays, (v) soft parton-to-hadron fragmentation functions, as well as
high-energy observables: (vi) global fits of parton distribution functions,
(vii) hard parton-to-hadron fragmentation functions, (viii) jets in p
DIS and -p photoproduction, (ix) photon structure function in
-, (x) event shapes and (xi) jet cross sections in
collisions, (xii) W boson and (xiii) Z boson decays, and (xiv) jets and (xv)
top-quark cross sections in proton-(anti)proton collisions. The current status
of the theoretical and experimental uncertainties associated to each extraction
method, the improvements expected from LHC data in the coming years, and future
perspectives achievable in collisions at the Future Circular Collider
(FCC-ee) with (1--100 ab) integrated luminosities yielding
10 Z bosons and jets, and 10 W bosons and leptons, are
thoroughly reviewed. The current uncertainty of the (preliminary) 2015 strong
coupling world-average value, = 0.1177 0.0013, is about
1\%. Some participants believed this may be reduced by a factor of three in the
near future by including novel high-precision observables, although this
opinion was not universally shared. At the FCC-ee facility, a factor of ten
reduction in the uncertainty should be possible, mostly thanks to
the huge Z and W data samples available.Comment: 135 pages, 56 figures. CERN-PH-TH-2015-299, CoEPP-MN-15-13. This
document is dedicated to the memory of Guido Altarell
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
We propose an experimental scheme to simulate the many-body dynamical quantum
Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice.
We first show that the required model Hamiltonian of a spin-1/2 Heisenberg
chain with an effective magnetic field and tunable parameters can be realized
in this system. For dynamical response to ramping the external fields, the
quantized plateaus emerge in the Berry curvature of the interacting atomic spin
chain as a function of the effective spin-exchange interaction. The
quantization of this response in the parameter space with the
interaction-induced topological transition characterizes the many-body
dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon
can be observed in practical cold-atom experiments with numerical simulations.Comment: 8 pages, 3 figures; accepted in Quantum Information Processin
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