Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpectral function and fidelity susceptibility in quantum critical phenomena
171
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we derive a simple equality that relates the spectral function $I(k,omega)$ and the fidelity susceptibility $chi_F$, i.e. $% chi_F=lim_{etarightarrow 0}frac{pi}{eta} I(0, ieta)$ with $eta$ being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy(ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.
rate research
Read More
We study fidelity susceptibility in one-dimensional asymmetric Hubbard model, and show that the fidelity susceptibility can be used to identify the universality class of the quantum phase transitions in this model. The critical exponents are found to be 0 and 2 for cases of half-filling and away from half-filling respectively.
We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilsons RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.
Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8~K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the electric polarization is a secondary order parameter at the lower-field (gap closure) quantum critical point but a primary one at the saturation transition. Having clearly identified the magnetic Bose-Einstein condensation (BEC) nature of the latter, we use the dielectric channel to directly measure the critical divergence of BEC susceptibility. The observed power-law behavior is in very good agreement with theoretical expectations for three-dimensional BEC. Finally, dielectric data reveal magnetic presaturation phases in this compound that may feature exotic order with unconventional broken symmetries.
Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).
We calculate numerically the fidelity and its susceptibility for the ground state of the Dicke model. A minimum in the fidelity identifies the critical value of the interaction where a quantum phase crossover, the precursor of a phase transition for finite number of atoms N, takes place. The evolution of these observables is studied as a function of N, and their critical exponents evaluated. Using the critical exponents the universal curve for the specific susceptibility is recovered. An estimate to the precision to which the ground state wave function is numerically calculated is given, and found to have its lowest value, for a fixed truncation, in a vicinity of the critical coupling.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
