Chiral Y junction of quantum spin chains

Abstract

We study a Y junction of spin-1/2 Heisenberg chains with an interaction that breaks both time-reversal and chain exchange symmetries, but not their product nor SU(2) symmetry. The boundary phase diagram features a stable disconnected fixed point at weak coupling and a stable three-channel Kondo fixed point at strong coupling, separated by an unstable chiral fixed point at intermediate coupling. Using non-abelian bosonization and boundary conformal field theory, together with density matrix renormalization group and quantum Monte Carlo simulations, we characterize the signatures of these low-energy fixed points. In particular, we address the boundary entropy, the spin conductance, and the temperature dependence of the scalar spin chirality and the magnetic susceptibility at the boundary. h B n d Q h w Z Q E P A M r / D m P D o v z r v z M W 8 t O P n M I f y B 8 / k D h C + P n A = = < / l a t e x i t > J < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 I Z Z 6 U M H d 4 D 0 X 9 s v v f d t 9 + 0 / G f o = " > A A A B 7 X i c d V D L S s N A F J 3 U V 6 2 v q k s 3 g 0 V w F Z I Y 2 r o r u h F X F e w D 2 l A m 0 0 k 7 d j I T Z i Z C C f 0 H N y 4 U c e v / u P N v n L Q V V P T A h c M 5 9 3 L v P W H C q N K O 8 2 E V V l b X 1 j e K m 6 W t 7 Z 3 d v f L + Q V u J V G L S w o I J 2 Q 2 R I o x y 0 t J U M 9 J N J E F x y E g n n F z m f u e e S E U F v 9 X T h A Q x G n E a U Y y 0 k d r X g z 4 e 0 0 G 5 4 t j n 9 a r n V 6 F j O 0 7 N 9 d y c e D X / z I e u U X J U w B L N Q f m 9 P x Q 4 j Q n X m C G l e q 6 T 6 C B D U l P M y K z U T x V J E J 6 g E e k Z y l F M V J D N r 5 3 B E 6 M M Y S S k K a 7 h X P 0 + k a F Y q W k c m s 4 Y 6 b H 6 7 e X i X 1 4 v 1 V E 9 y C h P U k 0 4 X i y K U g a 1 g P n r c E g l w Z p N D U F Y U n M r x G M k E d Y m o J I J 4 e t T + D 9 p e 7 b r 2 O 6 N X 2 l c L O M o g i N w D E 6 B C 2 q g A a 5 A E 7 Q A B n f g A T y B Z 0 t Y j 9 a L 9 b p o L V j L m U P w A 9 b b J 6 z A j z E = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 I Z Z 6 U M H d 4 D 0 X 9 s v v f d t 9 + 0 / G f o = " > A A A B 7 X i c d V D L S s N A F J 3 U V 6 2 v q k s 3 g 0 V w F Z I Y 2 r o r u h F X F e w D 2 l A m 0 0 k 7 d j I T Z i Z C C f 0 H N y 4 U c e v / u P N v n L Q V V P T A h c M 5 9 3 L v P W H C q N K O 8 2 E V V l b X 1 j e K m 6 W t 7 Z 3 d v f L + Q V u J V G L S w o I J 2 Q 2 R I o x y 0 t J U M 9 J N J E F x y E g n n F z m f u e e S E U F v 9 X T h A Q x G n E a U Y y 0 k d r X g z 4 e 0 0 G 5 4 t j n 9 a r n V 6 F j O 0 7 N 9 d y c e D X / z I e u U X J U w B L N Q f m 9 P x Q 4 j Q n X m C G l e q 6 T 6 C B D U l P M y K z U T x V J E J 6 g E e k Z y l F M V J D N r 5 3 B E 6 M M Y S S k K a 7 h X P 0 + k a F Y q W k c m s 4 Y 6 b H 6 7 e X i X 1 4 v 1 V E 9 y C h P U k 0 4 X i y K U g a 1 g P n r c E g l w Z p N D U F Y U n M r x G M k E d Y m o J I J 4 e t T + D 9 p e 7 b r 2 O 6 N X 2 l c L O M o g i N w D E 6 B C 2 q g A a 5 A E 7 Q A B n f g A T y B Z 0 t Y j 9 a L 9 b p o L V j L m U P w A 9 b b J 6 z A j z E = < / l a t e x i t > < l a t e x i t s ...

Spin Chain Network Construction of Chiral Spin Liquids

“…Remarkably, for a special value J χ = J c χ , one finds an ideal chiral fixed point where incoming spin currents are perfectly rerouted to the next chain in rotation, without any backscattering. For → ∞, the chiral point is unstable as it corresponds to a BCFT critical point [35,36]. We here show from density matrix renormalization group (DMRG) simulations that in networks of finite-length spin chains, the chiral fixed point remains present.…”

“…A single Y junction of spin-1/2 Heisenberg chains has been studied in Refs. [35,36]. The boundary conditions at this junction can be controlled by tuning a three-spin interaction J χ , see Fig.…”

“…w D K / w 5 k j n x X l 3 P h a t a 0 4 x c w J / 4 H z + A A 6 0 j j 8 = < / l a t e x i t > 2<l a t e x i t s h a 1 _ b a s e 6 4 = " M 9 s s q 0 1). At the chiral fixed point, Jχ = J c χ , incoming (left-moving, L) spin currents are perfectly rerouted in a counterclockwise (for Jχ > 0) sense [35,36]. (b) Adding Y junctions at each chain boundary x = , and iterating the process, one obtains the shown 2D spin chain network.…”

Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model

“…This phase diagram exhibits a variety of phases, including the chiral phase which appears in a relatively weak magnetic field regime [15]. Very recently, studying the so-called Y junctions made of spin-1/2 Heisenberg chains, it has been shown that a network of these junctions, with uniform coupling constants, may realize chiral spin liquid phases [16,17]. Remarkably, a controlled analytical investigation of these chiral spin liquid states may be realized by means of a honeycomb lattice of Heisenberg spin-1/2 chains, with three-spin Y junction interactions [18].…”

Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

“…18,21,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] The ground state properties of Y junctions have also been explored using density matrix renormalization group (DMRG) techniques. [51][52][53] A study of TDOS using bosonization technique for spinless fermion was reported by Agarwal et al in Ref. [18] and a collection of FPs (stable for g > 1) were identified which showed enhancement of TDOS in the zero energy limit and the effect was attributed to an Andreev-like reflection off the junction.…”