Factorization and Criticality in Finite XXZ Systems of Arbitrary Spin

Abstract

We analyze ground state (GS) factorization in general arrays of spins si with XXZ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GS's can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for d-dimensional arrays. The definite magnetization projected GS's at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.One of the most remarkable phenomena arising in finite interacting spin systems is that of factorization. For particular values and orientations of the applied magnetic fields, the system possesses a completely separable exact ground state (GS) despite the strong couplings existing between the spins. The close relation between GS factorization and quantum phase transitions was first reported in [1] and has since been studied in various spin models [2][3][4][5][6][7][8][9][10][11][12], with general conditions for factorization discussed in [7] and [13]. Aside from some well known integrable cases [14-17], higher dimensional systems of arbitrary spin in general magnetic fields are not exactly solvable, so that exact factorization points and curves provide a useful insight into their GS structure.The XXZ model is an archetypal quantum spin system which has been widely studied to understand the properties of interacting many-body systems and their quantum phase transitions [18][19][20][21][22][23] Our aim here is to show that in finite XXZ systems of arbitrary spin under nonuniform fields, highly degenerate exactly separable symmetry-breaking GS's can arise for a wide range of field configurations in arrays of any dimension, at an outstanding critical point where all magnetization plateaus merge and entanglement reaches full range. The Pokrovsky-Talapov (PT)-type transition in a spin-1/2 chain in an alternating field [20] is shown to correspond to this factorization. Magnetization phase diagrams, showing non trivial behavior at strong fields, and pair entanglement profiles for distinct factorization compatible field configurations are presented, together with analytic results for definite magnetization GS's.We consider an array of N spins s i interacting through XXZ couplings and immersed in a general nonuniform magnetic field along the z axis. The Hamiltonian readswith h i , S µ i the field and spin components at site i and J ij , J ij z the exchange coupling strengths. Since H commutes with the total spin component S z = i S z i , its eigenstates can be characterized by their total magnetization M along z. The exact GS will then exhibit definite M plateaus a...

Inducing critical phenomena in spin chains through sparse alternating fields

“…We set in what follows N = 2nK, with K the number of cells with 2n spins. A motivation for studying the field configurations (3) in the present system is that for j z > j > 0, they all exhibit, for any spin s ≥ 1/2, a multicritical point in the GS at fields of opposite sign given by [36]…”

“…Most investigations on nonuniform fields were focused so far on the alternating or "staggered" case [27][28][29][30][31][32][33][34][35]. Nonetheless, recent studies with more general nonuniform fields [35,36] have shown that interesting and significant phenomena can emerge, particularly with sparse field configurations [36].…”

Factorización y criticalidad en sistemas de espines

“…Con un argumento similar al presentado en la Sección 3.2.2 se puede demostrar que si ≥ 0 ∀ , , entonces el estado |Θ⟩ es el GS de con energía (5.11) [3].…”

“…Sin embargo, se sabe muy poco sobre las propiedades críticas que pueden ser inducidas en sistemas de espines a través de la aplicación de campos o acoplamientos no uniformes [1,3,90,[167][168][169][170]. Así pues, la gran mayoría de trabajos con campos no homogéneos analizan el caso de campos alternantes.…”

“…Finalmente, para > , las magnetizaciones | | < /2 solo pueden ser alcanzadas para campos de signo opuesto más allá del punto de factorización ℎ 1 = −ℎ 2 = ±ℎ , que es independiente de . Por el otro lado, cuando > el GS estará máximamente alineado ∀ aún cuando los campos son nulos; y los GS con menor magnetización | | < surgirán solamente para campos de signo opuesto más allá de los puntos de factorización determinados en el Capítulo 5 y dados por la ecuación (7.7) [3]. En este caso, las Ecs.…”