G. V. Shlyapnikov’s research while affiliated with Russian Quantum Center and other places

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Publications (222)


Adiabatic transformations in dissipative and non-Hermitian phase transitions
  • Article
  • Full-text available

February 2025

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2 Reads

Physical Review B

Pavel Orlov

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Georgy V. Shlyapnikov

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Denis V. Kurlov

The quantum geometric tensor has established itself as a general framework for the analysis and detection of equilibrium phase transitions in isolated quantum systems. We propose a generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian. We illustrate the proposed method by analyzing the non-Hermitian Su-Schrieffer-Heeger model and a generic quasifree dissipative fermionic system with a quadratic Liouvillian. Our findings reveal that this method effectively identifies phase transitions across all examined models, providing a universal tool for investigating general non-Hermitian systems. Published by the American Physical Society 2025

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Enhanced Drude weight in a one-dimensional system of fermions with pair-hopping events

May 2024

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21 Reads

In one dimension density-density interactions of particles reduce their mobility and hence the Drude weight, which controls the divergence of the optical conductivity at zero frequency, decreases. We study effects of pair-hopping events on this result in a one-dimensional system of spinless fermions. The considered model consists of the usual single-particle hopping and pair-hopping terms. In the absence of the density-density interactions, we first show that a variation of the pair-hopping amplitude results in a monotonic change of the Drude weight. We next demonstrate that weak nearest-neighbor density-density interactions increase the Drude weight, whereas in the regime of strong interactions the Drude weight decreases as expected. Our numerical findings are supported by bosonization results.


FIG. 1. (a) Schematic representation of the fermionic model (3). For J2/|J1| < 0 on top of single particle hoppings pair hopping events are also favoured, as sketched in (b).
FIG. 2. Numerical DMRG results for the sound velocity vs and the TLL parameter K(L = 128) versus κ. The inset shows the results of the fitting procedure of Eq. (37) at κ = −1.
Enhanced Drude weight in a 1D system of fermions with pair hopping events

January 2024

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73 Reads

In one dimension density-density interactions of particles reduce their mobility and hence the Drude weight, which controls the divergence of the optical conductivity at zero frequency, decreases. We study effects of pair hopping events on this result in a 1D system of spinless fermions. The considered model consists of the usual single-particle hopping and pair hopping terms. In the absence of the density-density interactions, we first show that a variation of the pair hopping amplitude results in a monotonic change of the Drude weight. We next demonstrate that weak nearest-neighbor density-density interactions increase the Drude weight, whereas in the regime of strong interactions the Drude weight decreases as expected. Our numerical findings are supported by bosonization results.


Tomonaga-Luttinger liquid–Bose-glass phase transition in a system of one-dimensional disordered fermions with pair hoppings

January 2024

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19 Reads

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1 Citation

We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical density matrix renormalization group calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose-glass phase, realizing the Giamarchi-Schulz scenario in such a system.


FIG. 1. (a) Schematic representation of the fermionic model (1). For J2/|J1| < 0 on top of single particle hoppings pair hopping events are also favoured, as sketched in (b).
Tomonaga-Luttinger liquid-Bose glass phase transition in a system of 1D disordered fermions with pair hoppings

August 2023

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116 Reads

We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical DMRG calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose glass phase, realising the Giamarchi-Schulz scenario in such a system.



Disordered impenetrable two-component fermions in one dimension

May 2023

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44 Reads

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3 Citations

D. V. Kurlov

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[...]

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G. V. Shlyapnikov

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t−0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t−0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.


Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases

December 2022

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16 Reads

We investigate the effect of weak disorder on the superfluid properties of two-component quasi-two-dimensional dipolar Fermi gases. The dipole-dipole interaction amplitude is momentum dependent, which violates the Anderson theorem claiming that the weak disorder has practically no influence on the superfluid transition temperature in the weakly interacting regime. For dipolar fermions the superfluid transition temperature in this regime can be strongly increased by the disorder. However, we find that the effect becomes smaller with increasing the intercomponent fermion-fermion interaction, and in the strongly interacting regime the superfluid transition temperature in the weak disorder becomes very close to that in the absence of disorder.



Rotons and their damping in elongated dipolar Bose-Einstein condensates

July 2022

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26 Reads

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1 Citation

Physical Review A

We discuss finite-temperature damping of rotons in elongated Bose-condensed dipolar gases, which are in the Thomas-Fermi regime in the tightly confined directions. The presence of many branches of excitations, which can participate in the damping process, is crucial for the Landau damping and results in significant increase of the damping rate. It is found, however, that even rotons with energies close to the roton gap may remain fairly stable in systems with the roton gap as small as 1nK.


Citations (52)


... In particular a pair hopping • • • ↔ • • • was introduced in [38] and later used in [39] to probe many-body mobility edges, and shown to be integrable in Ref. [25]. In [40] a similar constrained hopping term was shown to arise from the Jordan-Wigner transformation of a next nearest neighbor XY spin chain. Another constrained model recently studied is the socalled folded XXZ [16,21], where the ∆ → ∞ limit of the XXZ chain is considered, leading to integrable dynamics [22,23]. ...

Reference:

Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
Many-body localization transition in a frustrated XY chain
  • Citing Article
  • August 2022

... Since then, a range of exciting experiments explored patternformation and supersolidity in dBECs, including their excitation spectra [19][20][21][22][23], nucleation of vortices [24] and the emergence of patterns in elongated cigar-shaped traps with one-dimensional symmetry breaking [19,20,[25][26][27][28][29][30] and in a pancake trapping geometry, where the condensate is tightly confined along the polarization direction leading to a two-dimensionally broken symmetry [9,31]. This intense experimental activity has been complemented with a range of theoretical works exploring the physics of dBECs in cigar-shaped [32][33][34][35][36][37][38][39][40][41] and pancake traps [42][43][44][45][46][47][48]. ...

Rotons and their damping in elongated dipolar Bose-Einstein condensates
  • Citing Article
  • July 2022

Physical Review A

... Four papers [9][10][11][12] concern localization of matter waves and the properties of disordered quantum systems. Alain and his collaborators understood that laser speckle could provide a well-controlled disorder potential for ultracold atoms and in 2008 observed Anderson localization of a matter-wave in a one-dimensional system (1D). ...

Many-body localization of 1D disordered impenetrable two-component fermions
  • Citing Article
  • July 2022

The European Physical Journal D

... However, this theorem can be violated even on the mean-field level, for example, by the momentum dependence of the fermion-fermion scattering amplitude. As was pointed out in the recent work [18], the weak disorder can have a significant effect on the superfluid transition temperature of two-dimensional (2D) dipolar fermions with weak interactions. ...

Superfluid transition in disordered dipolar Fermi gases
  • Citing Article
  • November 2020

Physical Review A

... Our work could be considered as the first step towards realizing a proposal of Bazak and Petrov [22], where they showed that 39 K-40 K, as composite fermionic molecule with a boson lighter than a fermion, is a unique candidate to obtain a strongly p-wave-attractive Fermi gas in quasi-2D, thus providing a platform for studies of p-wave superfluidity. The sub-Doppler cooled mixture, as demonstrated here, could be used in optical tweezer experiments for the production of ultracold heteronuclear molecules [23], for the creation of mixed-species atom arrays [24] or, upon excitation to Rydberg states, as a medium for exploring strongly interacting multi-component fluids of light [25]. A fascinating research avenue opened up by the laser system design that can be explored in our experimental setup is the formation of triatomic heteronuclear fermionic molecules 39 K 40 K 41 K trapped in atomic arrays. ...

Coherently forming a single molecule in an optical trap
  • Citing Article
  • September 2020

Science

... Additionally, we observe spectroscopic phenomena, such as forbidden transitions and sideband transitions, in the superconducting fluxonium qubit, which are consistent with previous theoretical predictions [14,15]. Finally, due to the specific design parameters for this fluxonium, the higher energy levels in our heavy fluxonium exhibit extended decoherence times, making it particularly suitable for use as a qutrit [16][17][18][19] and qudit [20][21][22][23] in high-dimensional quantum computation [24][25][26][27]. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ...

Scalable quantum computing with qudits on a graph
  • Citing Article
  • February 2020

Physical Review A

... Further research is needed to develop quantum-specific algorithms that can be applied in various fields, such as biology, economics, and social sciences (Lostaglio, 2021). A more in-depth empirical evaluation is required to understand how quantum computing can be used in an operational context and deliver the desired results (Fedorov, 2019). This research shows that a more structured approach and a focus on practical applications can help direct research efforts in more productive and impactful directions. ...

Quantum technologies in Russia

... I discuss the phenomenology of the resulting critically localized regime, before concluding with a discussion of timescales upto which the regime may be expected to survive, which I argue are set by the avalanche. I work throughout on the lattice, avoiding the complications inherent with analyses in the continuum [14][15][16]. ...

Many-body localization in continuum systems: Two-dimensional bosons
  • Citing Article
  • July 2019

Physical Review A

... In the AAH model, when the quasiperiodic disorder strength exceeds a critical value, the Anderson localization transition occurs, causing all eigenstates to transition from extended states to localized states due to its self-duality. Later, it was demonstrated that in various generalized AAH models, the self-duality can be broken by introducing long-range hopping terms or modified quasiperiodic potentials, resulting in the exhibit of well-defined energy-dependent mobility edges [40][41][42][43][44][45]. The existence of the mobility edge implies that the system possesses an intermediate phase where the extended and localized states coexist in the energy spectrum, in addition to the extended phase where all eigenstates are extended and the localized phase where all eigenstates are localized. ...

One-Dimensional Quasicrystals with Power-Law Hopping
  • Citing Article
  • July 2019

Physical Review Letters

... The experimental investigation of Stoner ferromagnetism is hindered by the increase of three-body recombinations in the strongly-interacting regime of the upper branch [24][25][26]. Several mechanisms have been proposed to shift the ferromagnetic critical point to weaker interactions, including: adding shallow optical lattices [27,28], introducing disorder [29], tuning the mass imbalance [30][31][32], or including oddwave interactions [33][34][35]. Setups with reduced dimensionality have been considered as well [36][37][38][39][40], but various issues remain to be investigated, in particular for two-dimensional (2D) geometries. The studies on threedimensional (3D) systems found that, at large population imbalance, both attractive and repulsive Fermi gases are well described by the so-called Landau-Pomeranchuk energy functional [3,4,16,41]. ...

One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction
  • Citing Article
  • April 2019

Physical Review A