arXiv subjects

Dmitry Chernyak

Publications and source records attributed to Dmitry Chernyak.

9 recordsLinked to original sources

arXiv2026

What is the group of a quantum group? From $SL_q(2)$ to MPO representations of $SL(2)$

Generalized symmetries realized by matrix product operators (MPOs) have so far been tied to discrete data leaving continuous symmetries outside the framework. Quantum groups fill this gap: starting from the RTT relations of $SL_q(2)$ at an odd root of unity $q^d=1$, we construct a three-parameter family of periodic-boundary MPOs of bond dimension $d^2$ that multiply according to the group law of $SL(2)$. This gives Lusztig's quantum Frobenius map a concrete operator form, and endows the XXZ chain on the ring at $Δ=(q+q^{-1})/2$ with an intrinsically non-local $SU(2)$ symmetry. Fusion of the local tensors is generically semisimple. On special loci it is non-semisimple, and yields reducible but indecomposable tensors with Jordan blocks. Differentiating $\mathcal{D}(g)$ at the identity produces the $\mathfrak{sl}(2)$ generators as $d$-body operators: the MPO algebra supplies the exponential map for quantum group algebras.

cond-mat.stat-mech↗

arXiv2023

Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via $U_{\mathfrak{q}}\mathfrak{sl}_2$ Symmetry

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical difficulties due to the breaking of $\mathsf{U}(1)$ symmetry and the absence of a reference state are overcome by an algebraic construction where the two-boundary Temperley-Lieb Hamiltonian is realised in a new $U_{\mathfrak{q}}\mathfrak{sl}_2$-invariant spin chain involving infinite-dimensional Verma modules on the edges [J. High Energy Phys. 2022 (2022), no. 11, 016, 64 pages, arXiv:2207.12772]. The equivalence of the two Hamiltonians is established by proving Schur-Weyl duality between $U_{\mathfrak{q}}\mathfrak{sl}_2$ and the two-boundary Temperley-Lieb algebra. In this framework, the Nepomechie condition turns out to have a simple algebraic interpretation in terms of quantum group fusion rules.

hep-th↗

arXiv2022

$U_q\mathfrak{sl}_2$-invariant non-compact boundary conditions for the XXZ spin chain

We introduce new $U_q\mathfrak{sl}_2$-invariant boundary conditions for the open XXZ spin chain. For generic values of $q$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $q=e^{\frac{iπ}{p}}$ a $2p$-th root of unity $ - $ to its $p$-dimensional analogue. Both cases are parametrised by a continuous "spin" $α\in\mathbb{C}$. To motivate our construction, we first specialise to $q=i$, where we obtain a modified XX Hamiltonian with unrolled quantum group symmetry, whose spectrum and scaling limit is computed explicitly using free fermions. In the continuum, this model is identified with the $(η,ξ)$ ghost CFT on the upper-half plane with a continuum of conformally invariant boundary conditions on the real axis. The different sectors of the Hamiltonian are identified with irreducible Virasoro representations. Going back to generic $q$ we investigate the algebraic properties of the underlying lattice algebras. We show that if $q^α\notin\pm q^{\mathbb{Z}}$, the new boundary coupling provides a faithful representation of the blob algebra which is Schur-Weyl dual to $U_q\mathfrak{sl}_2$. Then, modifying the boundary conditions on both the left and the right, we obtain a representation of the universal two-boundary Temperley-Lieb algebra. The generators and parameters of these representations are computed explicitly in terms of $q$ and $α$. Finally, we conjecture the general form of the Schur-Weyl duality in this case. This paper is the first in a series where we will study, at all values of the parameters, the spectrum and its continuum limit, the representation content of the relevant lattice algebras and the fusion properties of these new spin chains.

hep-th↗

arXiv2022

First operation of undoped CsI directly coupled with SiPMs at 77 Kelvin

The light yield of a small undoped cesium iodide (CsI) crystal directly coupled with two silicon photomultipliers (SiPMs) at about 77~Kelvin was measured to be $43.0 \pm 1.1$~photoelectrons (PE) per keV electron-equivalent (keV$_\text{ee}$) using $X$ and $γ$-ray peaks from an $^{241}$Am radioactive source from 18 to 60 keV. The high light yield together with some other technical advantages illustrate the great potential of this novel combination for neutrino and low-mass dark matter detection, particularly at accelerator-based neutrino sources, where random background can be highly suppressed by requiring coincident triggers between SiPMs and beam pulse timing signals. Some potential drawbacks of using cryogenic SiPMs instead of photomultiplier tubes (PMTs) were identified, such as worse energy resolution and optical cross-talks between SiPMs. Their influence to rare-event detection was discussed and possible solutions were provided.

physics.ins-det↗

arXiv2020

Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains

We consider rational integrable supersymmetric gl(m|n) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra) defined by functional relations between Baxter Q-functions that we call Wronskian Bethe equations. These equations, in contrast to standard nested Bethe equations, admit only physical solutions for any value of inhomogeneities and furthermore we prove that the algebraic number of solutions to these equations is equal to the dimension of the spin chain Hilbert space (modulo relevant symmetries). Both twisted and twist-less periodic boundary conditions are considered, the isomorphism statement uses, as a sufficient condition, that the spin chain inhomogeneities $θ_\ell$, $\ell=1,\ldots,L$ satisfy $θ_\ell+\hbar\neqθ_{\ell'}$ for $\ell<\ell'$. Counting of solutions is done in two independent ways: by computing a character of the Wronskian algebra and by explicitly solving the Bethe equations in certain scaling regimes supplemented with a proof that the algebraic number of solutions is the same for any value of $θ_\ell$. In particular, we consider the regime $θ_{\ell+1}/θ_{\ell}\gg 1$ for the twist-less chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux.

math-ph↗

arXiv2020

Prospect of undoped inorganic scintillators at 77 Kelvin for the detection of non-standard neutrino interactions at the Spallation Neutron Source

Investigated in this work are sensitivities to non-standard neutrino interactions (NSI) of a prototype detector placed about 20 meters away from the Spallation Neutron Source at the Oak Ridge National Laboratory in two years of data taking. The presumed prototype consists of 10 kg undoped CsI scintillation crystals directly coupled with SiPM arrays operated at 77 K. Compared to the COHERENT CsI(Na) detector, a much higher light yield is assumed for the prototype. An experiment with a cylindrical undoped CsI crystal coupled directly to a photomultiplier tube at about 77 K was conducted to verify the light yield assumption. A yield of $33.5 \pm 0.7$ photoelectrons per keV electron-equivalent (PE/keVee) was achieved in [13, 60] keVee, which is much closer to the relevant energy region for the NSI search than some of the early studies.

physics.ins-det↗

arXiv2020

Prospect of undoped inorganic crystals at 77 Kelvin for low-mass dark matter search at Spallation Neutron Source

Investigated in this work were sensitivities of a prototype detector for the detection of low-mass dark matter particles produced at the Spallation Neutron Source at the Oak Ridge National Laboratory in two years of data taking. The presumed prototype consisted of 10 kg undoped CsI or NaI scintillation crystals directly coupled with SiPM arrays operated at 77 K. Compared to the COHERENT CsI(Na) detector, a much higher light yield was assumed for the prototype. An experiment with a cylindrical 1~kg undoped CsI crystal coupled directly to two photomultiplier tubes at about 77~K was conducted as the first step to verify the idea. A light yield of $26.0 \pm 0.4$ photoelectrons per keV electron-equivalent was achieved. This eliminated the concern of self light absorption in large crystals raised in some of the early studies.

physics.ins-det↗

arXiv2018

A large area detector for thermal neutron flux measurements at the KamLAND site

A large area (0.5~m $\times$ 0.5~m) thermal neutron detector was developed based on 0.32~mm-thick $^{6}$LiF:ZnS(Ag) scintillator sheets. The detector was constructed for measurements of seasonal variations in low intensity thermal neutron flux at deep underground sites. The detector response to neutrons was studied using a low intensity $^{241}$Am/$^{9}$Be($α$,n) neutron source. The digital pulse shape discrimination technique was applied to separate neutron capture events from the background caused by traces of $α$-emitters from Uranium and Thorium decay chains in scintillator components. The thermal neutron detection efficiency was 0.368$\pm$0.018 (0.155$\pm$0.009) before (after) event selection based on the digital pulse shape discrimination method. The measured $α$-particle background event rate in the $^{6}$LiF:ZnS(Ag) scintillator was (4.88$\pm$0.06(stat))$\times$10$^{-6}$ $α$ cm$^{-2}$sec$^{-1}$. As a test of detector performance we measured the thermal neutron flux at the KamLAND area of the Kamioka neutrino observatory and compared it with result of the neutron flux measurement carried out at the Super-Kamiokande site. The thermal neutron flux at KamLAND was (6.43$\pm$0.50)$\times$10$^{-6}$ n cm$^{-2}$sec$^{-1}$ that included $\sim$10~\% contribution from neutrons with energies above 1~eV. During the detector construction we identified a source of high amplitude noise pulses generated by 5-inch R1250 photomultipliers manufactured by Hamamatsu Photonics K. K..

physics.ins-det↗

arXiv2015

Development of cryogenic low background detector based on enriched zinc molybdate crystal scintillators to search for neutrinoless double beta decay of $^{100}$Mo

ZnMoO$_4$ scintillators with a mass of $\sim$ 0.3 kg, as well as Zn$^{100}$MoO$_4$ crystals enriched in the isotope $^{100}$Mo were produced for the first time by using the low-thermal-gradient Czochralski technique. The optical and luminescent properties of the produced crystals were studied to estimate the progress in crystal growth quality. The low-temperature tests with a 313 g ZnMoO$_4$ and two enriched Zn$^{100}$MoO$_4$ crystals were performed aboveground in the Centre de Sciences Nucléaires et de Sciences de la Matière. The low background measurements with a three ZnMoO$_4$ and two enriched detectors installed in the EDELWEISS set-up at the Laboratoire Souterrain de Modane were carried out. To optimize the light collection in ZnMoO$_4$ scintillating bolometers, we have simulated the collection of scintillation photons in a detector module for different geometries by Monte Carlo method using the GEANT4 package. Response to the 2$ν$2$β$ decay of $^{100}$Mo was simulated for the enriched Zn$^{100}$MoO$_4$ detectors of different shape and mass to understand the dependence of 2$ν$2$β$ decay spectra on crystal shape. We have simulated 48 Zn$^{100}$MoO$_4$ crystals with a size of Ø60 $\times$ 40 mm installed in the EDELWEISS cryostat. The contribution to background from the internal radioactive contamination of the crystals, cosmogenic activation and radioactive contamination of the set-up were simulated. Taking into account poor time resolution of the low temperature bolometers, we also studied contribution to background at the Q$_{2β}$ energy of random coincidences of signals, in particular of 2$ν$2$β$ decay, which is one of the main sources of background in cryogenic bolometers. Methods of the randomly coinciding events rejection were developed and compared. We have also analyzed dependence of the rejection efficiency on a cryogenic detector performance.

physics.ins-det↗