Zero-temperature Critical Behavior Research Articles

Coherence in quantum estimation

The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it establishes the ultimate bounds of the achievable precision. We show a relation between the statistical distance between infinitesimally close quantum states and the second order variation of the coherence of the optimal measurement basis with respect to the state of the probe. In quantum phase estimation protocols, this leads to propose coherence as the relevant resource that one has to engineer and control to optimize the estimation precision. Furthermore, the main object of the theory i.e. the symmetric logarithmic derivative, in many cases allows one to identify a proper factorization of the whole Hilbert space in two subsystems. The factorization allows one to discuss the role of coherence versus correlations in estimation protocols; to show how certain estimation processes can be completely or effectively described within a single-qubit subsystem; and to derive lower bounds for the scaling of the estimation precision with the number of probes used. We illustrate how the framework works for both noiseless and noisy estimation procedures, in particular those based on multi-qubit GHZ-states. Finally we succinctly analyze estimation protocols based on zero-temperature critical behavior. We identify the coherence that is at the heart of their efficiency, and we show how it exhibits the non-analyticities and scaling behavior proper of a large class of quantum phase transitions.

Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas

We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional strongly-correlated system: the integrable 1D Bose gas with repulsive \delta-function interaction (Lieb-Liniger model). Focusing on the observable dynamical density-density function, we present a Bethe Ansatz-based method allowing for its accurate evaluation over a broad range of momenta, frequencies, temperatures and interaction parameters, in finite but large systems. We show how thermal fluctuations smoothen the zero temperature critical behavior and present explicit quantitative results in experimentally accessible regimes.

ZERO-TEMPERATURE PHASE DIAGRAM OF DISSIPATIVE RANDOM ISING FERROMAGNETIC CHAINS

We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.

Finite-size scaling investigations in the quantum varphi4-model with long-range interaction

In this paper, we study in detail the critical behaviour of the (n ) quantum 4 -model with long-range interaction decaying with distances rby a power law as r-d - in the large-nlimit. The zero-temperature critical behaviour is discussed. Its alteration by finite temperature and/or finite sizes in the space is studied. The scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead. A number of results for the correlation length, critical amplitudes and the finite-size shift, for different dimensionalities between the lower d<= /2 and the upper d>= 3 /2 critical dimensions, are calculated.

Field theory of ferrimagnetic Hubbard chains

We present an extensive study of the ${\mathrm{AB}}_{2}$ polymeric Hubbard chains with experimental motivation in inorganic and organic compounds. In the half-filled strong-coupling limit, these systems can be mapped onto a quantum antiferromagnetic spin-$1/2 {\mathrm{AB}}_{2}$ Heisenberg model that presents a zero-temperature quantum phase transition to a ferrimagnetic ground state. We derive the spin-wave modes with the same correct ferromagnetic dispersion relation calculated through two different techniques. We also build an Euclidean integral formulation in the coherent state representation which naturally gives rise to Wess-Zumino terms of topological origin. The low-energy infrared behavior of the ${\mathrm{AB}}_{2}$ chains is properly described through a renormalization group analysis by the semiclassical fixed point of a one-dimensional quantum nonrelativistic nonlinear $\ensuremath{\sigma}$ model with critical dynamical exponent $z=2.$ Their low-temperature behavior is shown to be the same of a quantum ferromagnetic spin-1/2 Heisenberg chain, as evidenced by the temperature dependence of the correlation length, susceptibility, and specific heat. On the other hand, a quantum critical fixed point is also found, with the same zero-temperature critical behavior of a classical Heisenberg system in $D=d+z=3$ dimensions. Its low-temperature critical properties are related to the latter through the crossover exponent $\ensuremath{\varphi}=z{\ensuremath{\nu}}_{3},$ where ${\ensuremath{\nu}}_{3}$ is the correlation length exponent of the $D=3$ classical Heisenberg model. Sufficiently strong quantum critical fluctuations destroy the ordered ground state of the quantum $z=2$ nonlinear $\ensuremath{\sigma}$ model (but not that of the quantum ${\mathrm{AB}}_{2}$ Heisenberg spin systems, in agreement with a theorem by Lieb), giving rise to a quantum disordered phase at zero temperature. These results are supported by a connection between the quantum ${\mathrm{AB}}_{2}$ Heisenberg and generalized quantum rotor models.

Properties of a Luttinger liquid with boundaries at finite temperature and size

We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size, and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies $\ensuremath{\omega}$, with the spectral density scaling as ${\ensuremath{\omega}}^{2}$ for $\ensuremath{\omega}$ much less than the temperature. Consequences for photoemission experiments are discussed.

Dilute spin glass at zero temperature in general dimension.

We study the zero-temperature critical behavior of the dilute Ising spin glass. In our model nearest-neighbor exchange interactions randomly assume the values +J, 0, -J with probabilities p/2, 1-p, and p/2, respectively. We have generated 15th-order series for the Edwards-Anderson spin-glass susceptibility as a function of concentration p on hypercubic lattices in general dimension. Their analysis leads to critical concentrations and exponents that differ from those of percolation.

On the zero-temperature critical behaviour of the quantum X- Y model in a transverse magnetic field

It is shown that the zero-temperature critical behaviour of the quantum-mechanical X- Y spin model in a transverse magnetic field is characterized by pure gaussian critical exponents. Remarks on the university of the quantum critical behaviour are also made.

On the zero temperature critical behaviour of the nonideal Bose gas

The zero temperature renormalization group recursion relations, their fixed points and the corresponding critical exponents are obtained up to third order in the ϵ-expansion for the nonideal Bose gas in its functional formulation. The considerable simplifications in the zero temperature limit reveal the possibility for an infinite summation of the perturbation series.

On the zero temperature critical behaviour of the xy model in a transverse field

A previously developed bosonisation scheme is applied to the investigation of the zero-temperature critical behaviour of the XY model in a transverse field. It is shown how this method yields, in a simple and straightforward way, the results previously obtained using cumulants. The meaning of these results is briefly analysed.