Quantum Phase Transitions
نویسنده
چکیده
whereM is a real, symmetric, positive-definite matrix (i.e. all eigenvalues are positive). This identity can be easily established by changing variables of integration to a basis in which M is diagonal. We will use this identity to compute the free energy density F , defined by Z = exp(−V F ) where V is the volume of spacetime. In the paramagnetic phase, r > 0, the perturbative expansion for F takes the form F = C1 + C2u + O(u) + . . ., while in the magnetically ordered phase, r < 0, it takes the form F = C3/u+C4 +O(u). Obtain expressions for C1−4. Assume we have normalized the Dφα in Z to absorb the factor of 1/ √ π in (2).
منابع مشابه
سیستمهای ناکام و همبسته الکترونی
Quantum phases and fluctuations in correlated electron systems with frustration and competing interactions are reviewed. In the localized moment case the S=1/2 J1 - J2 - model on a square lattice exhibits a rich phase diagram with magnetic as well as exotic hidden order phases due to the interplay of frustration and quantum fluctuations. Their signature in magnetocaloric quantities and the hig...
متن کاملEnergy states and exchange energy of coupled double quantum dot in a magnetic field
The ground state energies of two interacting electrons confined in a coupled double quantum dot (DQD) presented in a magnetic field has been calculated by solving the relative Hamiltonian using variational and exact diagonalization methods. The singlet-triplet transitions in the angular momentum and spin of the quantum dot ground state had been shown .We have studied the magnetic field versus c...
متن کاملEnergy states and exchange energy of coupled double quantum dot in a magnetic field
The ground state energies of two interacting electrons confined in a coupled double quantum dot (DQD) presented in a magnetic field has been calculated by solving the relative Hamiltonian using variational and exact diagonalization methods. The singlet-triplet transitions in the angular momentum and spin of the quantum dot ground state had been shown .We have studied the magnetic field versus c...
متن کاملQuantum Phase Transitions
Phase transitions which occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed are called quantum phase transitions. They are caused by quantum fluctuations which are a consequence of Heisenberg’s uncertainty principle. These lecture notes give a pedagogical introduction to quantum phase transitions. After collecting a few basi...
متن کاملQuantum phase transitions in an array of coupled nanocavity quantum dots
We investigate exciton-photon quantum phase transitions in a planar lattice of one-mode cavities containing one quantum dot. The quantum dot can be occupied by up to two excitons with opposite spin. We adopt the well-established mean-field approximation comprising an exciton order parameter and a photon coherence parameter. Calculating excitonand photon-phase diagrams it is demonstrated that by...
متن کاملThermodynamic analogy for quantum phase transitions at zero temperature
We propose a relationship between thermodynamic phase transitions and groundstate quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and exceptional points of a quantum Hamiltonian in the complexextended parameter space. This approach is applied in the interacting boson model,...
متن کامل