arXiv subjects

Dmitri A. Ivanov

Publications and source records attributed to Dmitri A. Ivanov.

17 recordsLinked to original sources

arXiv2023

Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states

It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I extend this result to a generalization of the matrix permanent: an expectation value in a product of a large number of identical bosonic states with a bounded number of bosons. This result complements earlier studies on the computational complexity in boson sampling and related setups. The proposed technique based on the Gaussian averaging is equally applicable to bosonic and fermionic systems. This also allows us to improve an earlier polynomial complexity estimate for the fermionic version of the same problem.

quant-ph↗

arXiv2020

Complexity of full counting statistics of free quantum particles in product states

We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics problems. Depending on the initial multi-particle product state, the expectation values may be either easy to compute (the required number of operations scales polynomially with the particle number) or hard to compute (at least as hard as a permanent of a matrix). However, if we only consider full counting statistics in a finite number of final single-particle states, then the full-counting-statistics generating function becomes easy to compute in all the analyzed cases. We prove the latter statement for the general case of the fermionic product state and for the single-boson product state (the same as used in the boson-sampling proposal). This result may be relevant for using multi-particle product states as a resource for quantum computing.

quant-ph↗

arXiv2018

Atomtronics with a spin: statistics of spin transport and non-equilibrium orthogonality catastrophe in cold quantum gases

We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the non-equilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multi-step Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips.

cond-mat.quant-gas↗

arXiv2018

Universal many-body response of heavy impurities coupled to a Fermi sea

In this work we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate and prove that within the considered model the fastest rate of long-time decoherence is given by $γ=πk_BT/4$. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures $T/T_F\lesssim 0.2$ where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid $^3$He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several phenomena that can be tested using currently available experimental technology.

cond-mat.quant-gas↗

arXiv2017

Computational complexity of exterior products and multi-particle amplitudes of non-interacting fermions in entangled states

Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multi-particle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank two. In particular, a permanent of a NxN matrix may be expressed as an exterior product of N^2 two-forms of rank two in dimension 2N^2, which establishes the #P-hardness of the latter.

cs.CC↗

arXiv2015

Fermionic full counting statistics with smooth boundaries: from discrete particles to bosonization

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher--Hartwig expansion for Toeplitz determinants, while in the continuous limit we recover the bosonization results. This example of full counting statistics with smoothing is also related to orthogonality catastrophe, Fermi-edge singularity and non-equilibrium bosonization.

cond-mat.mes-hall↗

arXiv2013

Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain

Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painleve equations. We present explicit results up to eleventh order and compare them with a numerical example.

cond-mat.str-el↗

arXiv2013

Fisher-Hartwig expansion for Toeplitz determinants and the spectrum of a single-particle reduced density matrix for one-dimensional free fermions

We study the spectrum of the Toeplitz matrix with a sine kernel, which corresponds to the single-particle reduced density matrix for free fermions on the one-dimensional lattice. For the spectral determinant of this matrix, a Fisher--Hartwig expansion in the inverse matrix size has been recently conjectured. This expansion can be verified order by order, away from the line of accumulation of zeros, using the recurrence relation known from the theory of discrete Painleve equations. We perform such a verification to the tenth order and calculate the corresponding coefficients in the Fisher-Hartwig expansion. Under the assumption of the validity of the Fisher-Hartwig expansion in the whole range of the spectral parameter, we further derive expansions for an equation on the eigenvalues of this matrix and for the von Neumann entanglement entropy in the corresponding fermion problem. These analytical results are supported by a numerical example.

cond-mat.mes-hall↗

arXiv2013

Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit

We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the "counting parameter". We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients.

cond-mat.str-el↗

arXiv2013

Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains

We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the quantum XY chain, the method reproduces the previously known phase diagram.

cond-mat.str-el↗

arXiv2013

Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics

We consider the entanglement entropy for a line segment in the system of noninteracting one-dimensional fermions at zero temperature. In the limit of a large segment length L, the leading asymptotic behavior of this entropy is known to be logarithmic in L. We study finite-size corrections to this asymptotic behavior. Based on an earlier conjecture of the asymptotic expansion for full counting statistics in the same system, we derive a full asymptotic expansion for the von Neumann entropy and obtain first several corrections for the Renyi entropies. Our corrections for the Renyi entropies reproduce earlier results. We also discuss the entanglement spectrum in this problem in terms of single-particle occupation numbers.

cond-mat.mes-hall↗

arXiv2011

Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher--Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment. Unlike the method of bosonization, the Fisher--Hartwig formula correctly takes into account the discreteness of charge. Furthermore, we check numerically the precision of the generalized Fisher--Hartwig formula, find that it has a higher precision than rigorously proven so far, and conjecture the form of the next-order correction to the existing formula.

cond-mat.str-el↗

arXiv2011

Continuous interpolation between the fully frustrated Ising and quantum dimer models

We propose a new quantum model interpolating between the fully frustrated spin-1/2 Ising model in a transverse field and a dimer model. This model contains a resonating-valence-bond phase, including a line with an exactly solvable ground state of the Rokhsar-Kivelson type. We discuss the phase diagrams of this model on the square and triangular (in terms of the dimer representation) lattices.

cond-mat.str-el↗

arXiv2011

Vison excitations in near-critical quantum dimer models

We study vison excitations in a quantum dimer model interpolating between the Rokhsar-Kivelson models on the square and triangular lattices. In the square-lattice case, the model is known to be critical and characterized by U(1) topological quantum numbers. Introducing diagonal dimers brings the model to a Z_2 resonating-valence-bond phase. We study variationally the emergence of vison excitations at low concentration of diagonal dimers, close to the critical point. We find that, in this regime, vison excitations are large in size and their structure resembles vortices in type-II superconductors.

cond-mat.str-el↗

arXiv2010

Phase transitions in full counting statistics for periodic pumping

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The extensive part of the generating function can either be an analytic function on this circle or have singularities. These two cases may be interpreted as different thermodynamic phases in time domain. We discuss several examples of phase transitions between these phases for classical and quantum systems. Finally, we prove a criterion for the "analytic" phase in the problem of a quantum pump for noninteracting fermions.

cond-mat.mes-hall↗

arXiv2005

A Variational Monte Carlo Study of the Current Carried by a Quasiparticle

With the use of Gutzwiller-projected variational states, we study the renormalization of the current carried by the quasiparticles in high-temperature superconductors and of the quasiparticle spectral weight. The renormalization coefficients are computed by the variational Monte Carlo technique, under the assumption that quasiparticle excitations may be described by Gutzwiller-projected BCS quasiparticles. We find that the current renormalization coefficient decreases with decreasing doping and tends to zero at zero doping. The quasiparticle spectral weight Z_+ for adding an electron shows an interesting structure in k space, which corresponds to a depression of the occupation number k just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed.

cond-mat.str-el↗

arXiv1997

Bipolaronic charge excitations in t-J two-leg ladders

We present a low-energy effective model for the charge degrees of freedom in two-leg t-J ladders. Starting from SU(2) mean-field theory, we exclude the spin degrees of freedom which have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\sim 3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.

cond-mat↗