The Fermi gas model of one-dimensional conductors is reviewed. The exact solution known for particular values of the coupling constants in a single chain problem /Tomonaga model, Luther-Emery model/ are discussed. Renor malization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The rela tionship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed. АННОТАЦИЯ РассматриваетсяФерми-газ модель одномерных проводников. Обсуждают ся точные решения модели, существующие при определенных значениях константы связи в случае одной нити /модель Томонаги, модель Лютера-Эмери/. Метод группы ренормировок применяется для обобщения этих решений для произвольных значений константы связи. Исследуются свойства функции отклика для изучения возможных основных состояний и неустойчивостей. Обсуждается связь данной модели и других моделей и полученные соотношения используются для получения дальнейших инфор маций о свойствах системи. Модель далее обобщается на рассмотрение сети свя занных нитей чтобы изучить квази-одномерных систем. Обсуждается переход от одномерных свойств к трехмерным и тип упорядочения. KIVONATÁttekintést adunk az egydimenziós vezetők Fermi-gáz modelljéről. Az egylánc-problémában a csatolási állandók meghatározott értékénél /Tomonagamodell, Luther-Emery modell/ egzakt megoldások léteznek. A renormálási cso port segítségéve] ezeket a megoldásokat általánosíthatjuk a csatolások tet szőleges értékére. A válászfüggvények vizsgálatával tanulmányozzuk a rendszer instabilitásait és a lehetséges alapállapotokat. Tárgyaljuk a Fermi gáz mo dell és más modellek kapcsolatát!és felhasználjuk ezt, hogy további informá ciót kapjunk a rendszerről. Általánosítjuk a modellt a csatolt láncok rend szerére, hogy kváziegydimenziós rendszereket is leírhassunk. Tárgyaljuk az egydimenziós viselkedésből a háromdimenziós viselkedésbe történő átmenetet és a rendeződés tipusait.Luther-Emery line. Response functions of theLuther-Emery model. § 7. SCALING TO THE EXACTLY SOLUBLE MODELS. § 8. PHYSICAL PROPERTIES OF THE MODEL. 8.1. Phase diagram of the Fermi gas model. 8.2. Uniform susceptibility, compressibility and specific heat. 8.3. Temperature dependence of the conductivity. § 9. DIFFERENT CHOICES OF THE CUTOFF. 9.1. Scaling theories with two cutoffs. 9.2. Relationship between the physical cutoffs and the cutoff of the bosonized Hamiltonian. § 10. SOLUTION OF THE MODEL BELOW THE LUTHER-EMERY LINE. § 11. RELATIONSHIP BETWEEN THE FERMI GAS MODEL AND OTHER MODELS. 11.1. The two-dimensional Coulomb gas. 11.2. Spin models. 11.3. Field theoretical models. 11.4. The Hubbard model. 11.5. Summary of relationship of various models. § 12. SYSTEM...

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We have studied quantum data compression for finite quantum systems where the site density matrices are not independent, i.e., the density matrix cannot be given as direct product of site density matrices and the von Neumann entropy is not equal to the sum of site entropies. Using the density-matrix renormalization group (DMRG) method for the 1-d Hubbard model, we have shown that a simple relationship exists between the entropy of the left or right block and dimension of the Hilbert space of that block as well as of the superblock for any fixed accuracy. The information loss during the RG procedure has been investigated and a more rigorous control of the relative error has been proposed based on Kholevo's theory. Our results are also supported by the quantum chemistry version of DMRG applied to various molecules with system lengths up to 60 lattice sites. A sum rule which relates site entropies and the total information generated by the renormalization procedure has also been given which serves as an alternative test of convergence of the DMRG method.

We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group (DMRG) algorithm is used.PACS numbers: 71.10. Fd, 71.30.+h, 75.10.Jm The search for ground state and the study of quantum phase transitions (QPTs) is a challenging problem when strongly correlated fermionic or spin systems are considered. Since exactly solvable models are rare, in most cases the relevant part of the excitation spectrum, the order parameters characterizing the various phases, or eventually susceptibilities are determined numerically on finite chains and their thermodynamic limit is determined using the standard finite-size scaling method. Unfortunately in several cases no definite conclusions can be drawn even if the calculations are performed on rather long chains.In this letter, we propose a new approach to detect QPTs and to locate the quantum critical point in lowdimensional spin or fermionic models. It is based on studying the behavior of the von Neumann entropy of two neighboring sites in the middle of a long chain, which can be defined both for fermionic and spin models, and can be especially easily implemented when the densitymatrix renormalization-group (DMRG) algorithm [1] is used.The method is closely related to concepts in quantum information theory, which recently have attracted great attention in relation to QPTs. Wu et al. [2] have shown that quite generally QPTs are signalled by a discontinuity in some measure of entanglement in the quantum system. One such measure is the concurrence [3] which has been used by a number of authors [4,5,6,7,8,9,10] in their study of spin models. Since the concurrence is defined for spin-1/2 systems only, for higher spins or fermionic models another measure of entanglement is needed.The local measure of entanglement, the one-site entropy, which is obtained from the reduced density matrix ρ i at site i, has been proposed by Zanardi [11] and Gu et al.[12] to identify QPTs. Contrary to their expectation, in many cases, this quantity turns out to be insensitive to QPT. As an example let us consider the most general isotropic spin-1 chain model described by the HamiltonianIn 1D, the model can be solved exactly at θ = ±π/4 and θ = ±3π/4, and is known to have at least four different phases [13]. The ground state is ferromagnetic for θ < −3π/4 and θ > π/2, while in between the integrable points separate the Haldane phase, which exists in the range −π/4 < θ < π/4, from the dimerized and the quantum spin nematic phases, respectively. The existence of another phase, the quantum quadrupolar phase [14] near θ = −3π/4 is not settled yet [15]. These phases and the...