Article
Mathematics
Ryan Kinser, Jenna Rajchgot
Summary: This paper unifies the equivariant geometry of type D quiver representation varieties, double Grassmannians, and symmetric varieties GL(a + b)/GL(a) x GL(b), by translating results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant K-theory between these three families. These results are all obtained from a generalization of Zelevinsky's construction for type A quivers to the type D setting, by giving explicit embeddings with nice properties of homogeneous fiber bundles over type D quiver representation varieties into these symmetric varieties.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
A. Okounkov, A. Smirnov
Summary: We construct an analog of quantum dynamical Weyl group in the equivariant K-theory of arbitrary Nakajima quiver variety X. The fundamental groupoid of a periodic locally finite hyperplane arrangement in Pic(X) circle times C serves as the correct generalization of the Weyl group in this context. The lattice part of this groupoid is identified with the operators of quantum difference equation for X. Examples are provided to illustrate the cases of quivers of finite and affine type.
INVENTIONES MATHEMATICAE
(2022)
Article
Mathematics
Andrey Smirnov, Zijun Zhou
Summary: In this study, we investigate the vertex functions for hypertoric varieties and their application in 3D mirror pairs. By examining the equivalence of two sets of q-difference equations, we establish a relationship between the exchanged Kahler and equivariant parameters and the opposite choice of polarization. Additionally, we discuss various notions of quantum K-theory for hypertoric varieties.
ADVANCES IN MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Ahana Chakraborty, Rajdeep Sensarma
Summary: This study introduces a new field theoretic method for calculating Renyi entropy of interacting bosons in subsystems without using replica methods. The method can be applied to dynamics of open and closed quantum systems, and can determine the relationship between the initial state and final density matrix to predict the behavior of entropy over time. The approach also shows that the entropy in non-Markovian dynamics approaches a steady-state value with exponents determined by nonanalyticities of the system's environment.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Harold Ollivier
Summary: We investigate the emergence of objectivity for quantum many-body systems in the absence of environmental interference. We extend the findings of Reidel (2017) to the case where the system is in a mixed state, measurements are performed using POVMs, and the measurement outcomes are imperfect. By introducing a new condition on states and measurements, we are able to achieve complete classicality for any number of observers. Furthermore, we demonstrate that the evolution of quantum many-body systems is expected to yield states satisfying this condition when the corresponding measurement outcomes are redundant.
Article
Computer Science, Interdisciplinary Applications
Justin A. Reyes, Dan C. Marinescu, Eduardo R. Mucciolo
Summary: This paper explores the exact computation of tensor network contractions on two-dimensional geometries and presents a heuristic improvement to reduce computing time, memory usage, and communication time. The results demonstrate that cloud computing is a viable alternative to supercomputers for scientific applications of this nature.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Materials Science, Multidisciplinary
Christian P. Chen, Henning Schomerus
Summary: By adopting a geometric perspective on Fock space, this study provides insights into the eigenstates in many-body localized fermionic systems. It reveals that individual many-body localized eigenstates can be well approximated by a Slater determinant of single-particle orbitals, while the orbitals of different eigenstates in a given system exhibit varying degrees of compatibility. This incompatibility between states of fixed and differing particle number, as well as inside and outside the many-body localized regime, offers detailed insights into the emergence and nature of quasiparticlelike excitations in such systems.
Article
Mathematics
Hunter Dinkins, Andrey Smirnov
Summary: In this paper, we investigate the capped vertex functions associated with certain zero-dimensional type -A Nakajima quiver varieties. We derive explicit combinatorial formulas for the capped vertex functions by inserting descendants using the Macdonald operators. We determine the monodromy of the vertex functions and establish its coincidence with the elliptic R-matrix of the symplectic dual variety. We also apply our findings to compute the vertex functions and characters of tautological bundles on quiver varieties formed from arbitrary stability conditions.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics
Yongbin Ruan, Yaoxiong Wen, Zijun Zhou
Summary: This paper introduces a new version of 3d mirror symmetry for the toric quotient stack [Cn/K], which is inspired by a 3d N = 2 abelian mirror symmetry construction in physics. The paper proves the mirror conjecture that the I-functions of a mirror pair coincide under the mirror map.
ADVANCES IN MATHEMATICS
(2022)
Article
Physics, Condensed Matter
Alexandre M. Souza, Roberto S. Sarthour, Ivan S. Oliveira
Summary: Entanglement has been an area of great interest since the early years of quantum mechanics. In recognition of their efforts in verifying the properties of entangled photons, the Nobel Prize in Physics for 2022 was awarded to Alain Aspect, John F. Clauser, and Anton Zeilinger, who are leading pioneers in this field. However, entanglement is not limited to photons and can occur among hundreds, millions, or even more particles in condensed matter systems. Quantum entanglement leads to strong non-classical correlations among particles, playing a crucial role in various properties of matter such as superconductivity and different forms of magnetic order that arise from highly correlated ground states in many-body systems.
PHYSICA B-CONDENSED MATTER
(2023)
Article
Materials Science, Multidisciplinary
Adam Nahum, Sthitadhi Roy, Sagar Vijay, Tianci Zhou
Summary: We study the real-time correlators of local operators in chaotic quantum many-body systems. These correlators exhibit universal structure at late times, determined by the geometry of the dominant operator-space Feynman trajectories. The decay of local correlations in the absence of conservation laws is described by rate functions associated with spacetime structures. In 1+1D, the operator histories can exhibit a phase transition, leading to singular behavior in the rate function. In higher-dimensional systems, thin trajectories always dominate. We also discuss the deducibility of butterfly velocity from time-ordered two-point functions and the computation of correlators in random circuits.
Article
Mathematics
Ming Lu, Weiqiang Wang
Summary: The paper explores the applications of iota quiver algebras and Dynkin miniver algebras in the Nakajima-Keller-Scherotzke categories, and provides a geometric construction of universal iota quantum groups for quantum symmetric pairs.
ADVANCES IN MATHEMATICS
(2021)
Article
Optics
Igor Ermakov, Boris Fine
Summary: Revivals of initial nonequilibrium states are a key focus in the theory of dynamic thermalization in many-body quantum systems. This study demonstrates how to construct a quantum state in a nonintegrable lattice of interacting spin 1/2 particles, leading to maximal initial polarization and almost complete recovery at a predetermined point in time. Experimental observation of these revivals can be used to benchmark quantum simulators with just one local observable measurement, and potentially for delayed disclosure of a secret.
Article
Optics
Raffaele Salvia, Vittorio Giovannetti
Summary: This study explores the influence of correlations in noninteracting quantum systems on energy extraction. In systems with a large number of sites, complete energy extraction can be achieved with relatively weak correlations. This effect is independent of quantum correlations and can be achieved using only incoherent energy ergotropy.
Article
Optics
Carlos Pineda, David Davalos, Carlos Viviescas, Antonio Rosado
Summary: Using the quantum map formalism, a framework is provided to construct fuzzy and coarse-grained quantum maps for many-body systems that consider limitations in measurement device resolution. These maps are applied to a spin-1/2 XX chain to obtain a blurred picture of entanglement generation and propagation. It is shown that the volume of tomographically accessible states decreases at a double-exponential rate with the number of particles, imposing severe bounds on the ability to read and use information from a many-body quantum system.
