arXiv subjects

Kiryl Pakrouski

Publications and source records attributed to Kiryl Pakrouski.

14 recordsLinked to original sources

arXiv2026

Exact group invariant scar towers in two dimensional gauge theories

We construct exact many-body scar towers in two dimensional gauge theories with two flavors of massless fundamental fermions. For oppositely charged fermions, the scar subspace is generated by a gauge-neutral $η$-pairing operator, and admits a purely algebraic construction. Exact diagonalization methods reveal anomalously low entanglement and long-range pair correlations in the scar states. Charge conjugation maps the $η$-tower to a vector-flavor polarization sector of the equal charge model, yielding an interpretation as a coherent flavor mode with Josephson-like phase dynamics. Finite fermion masses mix the protected pair with an orthogonal channel and destroy the exact tower. The identified scar tower can be algebraically realized in a large family of lattice field theories, revealing a universal character of these states. Our results provide an analytical construction of invariant scar subspaces in a gauge theory with a nontrivial continuum interpretation.

hep-th↗

arXiv2026

Certain BCS wavefunctions are quantum many-body scars

We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $η$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

cond-mat.str-el↗

arXiv2026

Unconventional superconducting correlations in fermionic many-body scars

Weak ergodicity breaking in interacting quantum systems may occur due to the existence of a subspace dynamically decoupled from the rest of the Hilbert space. In two-orbital spinful lattice systems, we construct such subspaces that are in addition distinguished by strongest inter-orbital and spin-singlet or spin-triplet, long-range superconducting pairing correlations. All unconventional pairing types we consider are local in space and unitary. Alternatively to orbitals, the additional degree of freedom could originate from the presence of two layers or through any other mechanism. Required Hamiltonians are rather non-exotic and include chemical potential, Hubbard, and spin-orbit interactions typically used for two-orbital superconducting materials. Each subspace is spanned by a family of group-invariant quantum many-body scars combining both 2e and 4e pairing/clustering contributions. One of the basis states has the form of a BCS wavefunction and can always be made the ground state by adding a mean-field pairing potential. Analytical results in this work are lattice-, dimension- and (mostly) system size-independent. We confirm them by exact numerical diagonalization in small systems.

cond-mat.str-el↗

arXiv2024

Stability of the many-body scars in fermionic spin-1/2 models

We study the stability of the many-body scars in spin-1/2 fermionic systems under the most typical perturbations in relevant materials. We find that some families of scars are completely insensitive to certain perturbations. In some other cases they are stable to the first order in perturbation theory. Our analytical results apply to a large class of Hamiltonians that are known [arXiv:2106.10300] to support exact many-body scars. For the numerical calculations we choose the deformed $t-J-U$ model that includes both Heisenberg and Hubbard interactions. We propose two new stability measures that are based on physical observables rather than the fidelity to the exact initial wavefunction. They enable the experimental detection of scars and are more reliable from the theoretical and numerical perspectives. One of these measures may potentially find applications in other systems where the exact many-body scars are equally spaced in energy. In small systems and at small perturbations, a regime particularly relevant for quantum simulators, we identify and describe an additional stability exhibited by the many-body scars. For larger perturbation strengths we observe a distinct mode of ergodicity breaking that is consistent with many-body localization.

cond-mat.str-el↗

arXiv2022

Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction

We present two 2-body Hamiltonians that approximate the exact PH-Pfaffian wavefunction with their ground states for all the system sizes where this wavefunction has been numerically constructed to date. The approximate wavefunctions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimisation procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a non-interacting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the PH-Pfaffian. We diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the PH-Pfaffian shift appears energetically more favorable. Possibility to interpret the data in terms of composite fermions is discussed.

cond-mat.str-el↗

arXiv2021

Group theoretic approach to many-body scar states in fermionic lattice models

It has been shown [arXiv:2007.00845] that three families of highly symmetric states are many-body scars for any spin-1/2 fermionic Hamiltonian of the form $H_0+OT$, where $T$ is a generator of an appropriate Lie group. One of these families consists of the well-known $η$-pairing states. In addition to having the usual properties of scars, these families of states are insensitive to electromagnetic noise and have advantages for storing and processing quantum information. In this paper we show that a number of well-known coupling terms, such as the Hubbard and the Heisenberg interactions, and the Hamiltonians containing them, are of the required form and support these states as scars without fine-tuning. The explicit $H_0+OT$ decomposition for a number of most commonly used models, including topological ones, is provided. To facilitate possible experimental implementations, we discuss the conditions for the low-energy subspace of these models to be comprised solely of scars. Further, we write down all the generators $T$ that can be used as building blocks for designing new models with scars, most interestingly including the spin-orbit coupled hopping and superconducting pairing terms. We expand this framework to the non-Hermitian open systems and demonstrate that for them the scar subspace continues to undergo coherent time evolution and exhibit the "revivals". A full numerical study of an extended 2D $tJU$ model explicitly illustrates the novel properties of the invariant scars and supports our findings.

cond-mat.str-el↗

arXiv2021

Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect

We present a method for the exact construction of the fully particle-hole symmetric PH-Pfaffian ground state and its charged excitations on a sphere. We adopt the Moore-Read state, but with a nonholomorphic pairing component as in previous studies, and project it to the lowest Landau level. We study the energetics as well as other properties of these states and find that in a pure system interacting with the Coulomb forces the PH-Pfaffian cannot compete with either the Moore-Read state or its particle-hole conjugate, the anti-Pfaffian state, as an explanation for the 5/2-effect.

cond-mat.mes-hall↗

arXiv2020

Many Body Scars as a Group Invariant Sector of Hilbert Space

We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of thermalization and the "revivals" of special initial states in time evolution. Some of the scar states found in earlier work may be viewed as special cases of our construction. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of $N$ sites (it includes deformations of the Fermi-Hubbard model as special cases), and we show that it contains two families of $N+1$ scar states. One of these families, which was found in recent literature, is comprised of the well-known $η$-pairing states. We find another family of scar states which is $U(N)$ invariant. Both families and most of the group-invariant scar states produced by our construction in general, give rise to the off-diagonal long range order which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored non-locally, and thus cannot be easily erased by local perturbations. In contrast, other scar states we find are product states which could be easily prepared experimentally. The dimension of scar subspace is directly controlled by the choice of group $G$ and can be made exponentially large.

cond-mat.str-el↗

arXiv2020

Automatic design of Hamiltonians

We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties specifying thereby the search query. Using fractional quantum Hall effect as a test system we illustrate how the framework can be used to determine a generating Hamiltonian of a finite-size model wavefunction (Moore-Read Pfaffian and Read-Rezayi states), find optimal conditions for an experiment or "extrapolate" given wavefunctions in a certain universality class from smaller to larger system sizes. We also discuss how the search for approximate generating Hamiltonians may be used to find simpler and more realistic models implementing the given exotic phase of matter by experimentally accessible interaction terms.

quant-ph↗

arXiv2020

Hagedorn Temperature in Large $N$ Majorana Quantum Mechanics

We discuss two types of quantum mechanical models that couple large numbers of Majorana fermions and have orthogonal symmetry groups. In models of vector type, only one of the symmetry groups has a large rank. The large $N$ limit is taken keeping $gN=λ$ fixed, where $g$ multiplies the quartic Hamiltonian. We introduce a simple model with $O(N)\times SO(4)$ symmetry, whose energies are expressed in terms of the quadratic Casimirs of the symmetry groups. This model may be deformed so that the symmetry is $O(N)\times O(2)^2$, and the Hamiltonian reduces to that studied in arXiv:1802.10263. We find analytic expressions for the large $N$ density of states and free energy. In both vector models, the large $N$ density of states varies approximately as $e^{-|E|/λ}$ for a wide range of energies. This gives rise to critical behavior as the temperature approaches the Hagedorn temperature $T_{\rm H} = λ$. In the formal large $N$ limit, the specific heat blows up as $(T_H- T)^{-2}$, which implies that $T_H$ is the limiting temperature. However, at any finite $N$, it is possible to reach arbitrarily large temperatures. Thus, the finite $N$ effects smooth out the Hagedorn transition. We also study models of matrix type, which have two $O(N)$ symmetry groups with large rank. An example is provided by the Majorana matrix model with $O(N)^2\times O(2)$ symmetry, which was studied in arXiv:1802.10263. In contrast with the vector models, the density of states is smooth and nearly Gaussian near the middle of the spectrum.

hep-th↗

arXiv2019

Spectrum of Majorana Quantum Mechanics with $O(4)^3$ Symmetry

We study the quantum mechanics of 3-index Majorana fermions $ψ^{abc}$ governed by a quartic Hamiltonian with $O(N)^3$ symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large $N$ limit dominated by the melonic diagrams. For $N=4$ the total number of states is $2^{32}$, but they naturally break up into distinct sectors according to the charges under the $U(1)\times U(1)$ Cartan subgroup of one of the $O(4)$ groups. The biggest sector has vanishing charges and contains over $165$ million states. Using a Lanczos algorithm, we determine the spectrum of the low-lying states in this and other sectors. We find that the absolute ground state is non-degenerate. If the $SO(4)^3$ symmetry is gauged, it is known from earlier work that the model has $36$ states and a residual discrete symmetry. We study the discrete symmetry group in detail; it gives rise to degeneracies of some of the gauge singlet energies. We find all the gauge singlet energies numerically and use the results to propose exact analytic expressions for them.

hep-th↗

arXiv2016

Experimental Signatures of the Inverted Phase in InAs/GaSb Coupled Quantum Wells

Transport measurements are performed on InAs/GaSb double quantum wells at zero and finite magnetic fields applied parallel and perpendicular to the quantum wells. We investigate a sample in the inverted regime where electrons and holes coexist, and compare it with another sample in the non-inverted semiconducting regime. Activated behavior in conjunction with a strong suppression of the resistance peak at the charge neutrality point in a parallel magnetic field attest to the topological hybridization gap between electron and hole bands in the inverted sample. We observe an unconventional Landau level spectrum with energy gaps modulated by the magnetic field applied perpendicular to the quantum wells. This is caused by strong spin-orbit interaction provided jointly by the InAs and the GaSb quantum wells.

cond-mat.mes-hall↗

arXiv2016

The enigmatic 12/5 fractional quantum Hall effect

We numerically study the fractional quantum Hall effect at filling factors $ν=12/5$ and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width and Landau level mixing. We find that Landau level mixing suppresses $ν=13/5$ fractional quantum Hall effect relative to $ν=12/5$. By contrast, we find both $ν=2/5$ and (its particle-hole conjugate) $ν=3/5$ fractional quantum Hall effects in the lowest Landau level to be robust under Landau level mixing and finite well-width corrections. Our results provide a possible explanation for the experimental absence of the 13/5 fractional quantum Hall state as caused by Landau level mixing effects.

cond-mat.str-el↗

arXiv2014

The Phase Diagram of the $ν=5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width

Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the $ν= 5/2$ fractional quantum Hall state. But the significant controversy surrounding the nature of the $ν= 5/2$ state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the $ν= 5/2$ state we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau level mixing into account to lowest-order perturbatively in $κ$, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate non-zero width $w$ of the quantum well and sub-band mixing. We find the ground state in both the torus and spherical geometries as a function of $κ$ and $w$. To sort out the non-trivial competition between candidate ground states we analyze the following 4 criteria: its overlap with trial wave functions; the magnitude of energy gaps; the sign of the expectation value of an order parameter for particle-hole symmetry breaking; and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for $κ< {κ_c}(w)$, where ${κ_c}(w)$ is a $w$-dependent critical value $0.6 \lesssim{κ_c}(w)\lesssim 1$. We observe that both Landau level mixing and non-zero width suppress the excitation gap, but Landau level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.

cond-mat.str-el↗